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Major upgrade merged from Trunk: see history section in the docs for the full details.

Browse Source 
[SVN r53183]
This commit is contained in:
John Maddock
2009-05-22 17:49:00 +00:00
parent 05ad60a8c9 62744fed77
commit 4c6c317588
688 changed files with 29281 additions and 4338 deletions
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31
build/Jamfile.v2
View File

@@ -4,6 +4,9 @@
# http://www.boost.org/LICENSE_1_0.txt.
import testing ;
import pch ;
cpp-pch pch : ../src/tr1/pch.hpp : <include>../src/tr1 <link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1 ;
C99_SOURCES = acosh
asinh
@@ -56,40 +59,44 @@ if --disable-long-double in [ modules.peek : ARGV ]
long-double-opts = <build>no ;
}
compile has_long_double_support.cpp : $(long-double-opts) ;
lib boost_math_tr1 : ../src/tr1/$(TR1_SOURCES).cpp
lib boost_math_tr1 : ../src/tr1/$(TR1_SOURCES).cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<include>../src/tr1
;
lib boost_math_tr1f : ../src/tr1/$(TR1_SOURCES)f.cpp
lib boost_math_tr1f : ../src/tr1/$(TR1_SOURCES)f.cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<include>../src/tr1
;
lib boost_math_tr1l : ../src/tr1/$(TR1_SOURCES)l.cpp
lib boost_math_tr1l : ../src/tr1/$(TR1_SOURCES)l.cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<dependency>has_long_double_support
$(long-double-opts)
<dependency>../config//has_long_double_support
<include>../src/tr1
$(long-double-opts)
;
lib boost_math_c99 : ../src/tr1/$(C99_SOURCES).cpp
lib boost_math_c99 : ../src/tr1/$(C99_SOURCES).cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<include>../src/tr1
;
lib boost_math_c99f : ../src/tr1/$(C99_SOURCES)f.cpp
lib boost_math_c99f : ../src/tr1/$(C99_SOURCES)f.cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<include>../src/tr1
;
lib boost_math_c99l : ../src/tr1/$(C99_SOURCES)l.cpp
lib boost_math_c99l : ../src/tr1/$(C99_SOURCES)l.cpp pch
:
<link>shared:<define>BOOST_MATH_TR1_DYN_LINK=1
<dependency>has_long_double_support
$(long-double-opts)
<dependency>../config//has_long_double_support
<include>../src/tr1
$(long-double-opts)
;

20
config/Jamfile.v2 Normal file
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@@ -0,0 +1,20 @@
# copyright John Maddock 2008
# Distributed under the Boost Software License, Version 1.0.
# (See accompanying file LICENSE_1_0.txt or copy at
# http://www.boost.org/LICENSE_1_0.txt.
import modules ;
import path ;
local ntl-path = [ modules.peek : NTL_PATH ] ;
local gmp_path = [ modules.peek : GMP_PATH ] ;
obj has_long_double_support : has_long_double_support.cpp ;
obj has_mpfr_class : has_mpfr_class.cpp :
<include>$(gmp_path) <include>$(gmp_path)/mpfr <include>$(gmp_path)/gmpfrxx ;
obj has_ntl_rr : has_ntl_rr.cpp : <include>$(ntl-path)/include ;

0
build/has_long_double_support.cpp → config/has_long_double_support.cpp
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14
config/has_mpfr_class.cpp Normal file
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@@ -0,0 +1,14 @@
// Copyright John Maddock 2008.
// Copyright Paul A. Britow 2009
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifdef _MSC_VER
# pragma warning (disable : 4127) // conditional expression is constant
# pragma warning (disable : 4800) // 'int' : forcing value to bool 'true' or 'false' (performance warning)
# pragma warning (disable : 4512) // assignment operator could not be generated
#endif
#include <gmpfrxx.h>

12
config/has_ntl_rr.cpp Normal file
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@@ -0,0 +1,12 @@
// Copyright John Maddock 2008.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifdef _MSC_VER
# pragma warning (disable : 4100) // unreferenced formal parameter
#endif
#include <NTL/RR.h>

3
doc/complex/Jamfile.v2
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@@ -62,7 +62,6 @@ boostbook standalone
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
<format>pdf:<xsl:param>draft.mode="no"
;
@@ -78,3 +77,5 @@ boostbook standalone

60
doc/distexplorer/Jamfile.v2 Normal file
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@@ -0,0 +1,60 @@
# Copyright Paul A. Bristow 2008
# Copyright John Maddock 2008
# Distributed under the Boost Software License, Version 1.0.
# (See accompanying file LICENSE_1_0.txt
# or copy at http://www.boost.org/LICENSE_1_0.txt)
# Reminder: whitespace MUST terminate variable name!
# so space BEFORE ; and :
# Distexplorer documentation as html from Quickbook.
# project boost/doc ;
using quickbook ;
#path-constant images_location : html ;
# location of SVG images referenced by Quickbook.
# screenshots installed as recomended by Sourceforge.
xml distexplorer
:
distexplorer.qbk
:
;
# import boostbook : boostbook ;
boostbook standalone
:
distexplorer
:
# Path for links to Boost:
<xsl:param>boost.root=../../../../..
# Path for libraries index:
<xsl:param>boost.libraries=../../../../../libs/libraries.htm
# Use the main Boost stylesheet:
<xsl:param>html.stylesheet=../../../../../doc/html/boostbook.css
# Some general style settings:
<xsl:param>table.footnote.number.format=1
<xsl:param>footnote.number.format=1
# HTML options first:
# Use graphics not text for navigation:
<xsl:param>navig.graphics=1
# How far down we chunk nested sections, basically all of them:
<xsl:param>chunk.section.depth=10
# Don't put the first section on the same page as the TOC:
<xsl:param>chunk.first.sections=1
# How far down sections get TOC's
<xsl:param>toc.section.depth=10
# Max depth in each TOC:
<xsl:param>toc.max.depth=4
# How far down we go with TOC's
<xsl:param>generate.section.toc.level=10
#<xsl:param>root.filename="distexplorer"
;

105
doc/distexplorer/distexplorer.qbk Normal file
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@@ -0,0 +1,105 @@
[article Statistical Distribution Explorer
[quickbook 1.4]
[copyright 2008 Paul A. Bristow, John Maddock]
[license
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
[@http://www.boost.org/LICENSE_1_0.txt])
]
[authors [Bristow, Paul A.], [Maddock, John]]
[category math]
[purpose mathematics]
[/last-revision $Date$]
]
A Windows utility to show the properties of statistical distributions
using parameters provided interactively by the user.
The distributions provided are:
*bernoulli
*beta_distribution
*binomial_distribution
*cauchy
*chi_squared
*exponential
*extreme_value
*fisher_f
*gamma_distribution
*lognormal_distribution
*negative_binomial_distribution
*normal_distribution
*pareto
*poisson
*rayleigh
*students_t
*triangular
*uniform
*weibull
Properties of distributions computed are:
*mean
*mode
*median
*variance
*standard deviation
*coefficient of variation,
*skewness
*kurtosis
*excess
*range supported
Calculated, from values provided, are:
*probability density (or mass) function (PDF)
*cumulative distribution function (CDF), and complement
*Quantiles (percentiles) are calculated for typical risk (alpha) probabilities (0.001, 0.01, 0.5, 0.1, 0.333)
and for additional probabilities provided by the user.
Results can be saved to text files using Save or SaveAs.
All the values on the four tabs are output to the file chosen,
and are tab separated to assist input to other programs,
for example, spreadsheets or text editors.
Note: Excel (for example), only shows 10 decimal digits, by default:
to display the maximum possible precision (abotu 15 decimal digits),
it is necessary to format all cells to display this precision.
Although unusually accurate, not all values computed by Distexplorer will be as accurate as this.
Values shown as NaN cannot be calculated from the value(s) given,
most commonly because the value input is outside the range for the distribution.
For more information, including downloads, see
[@http://distexplorer.sourceforge.net/ Distexplorer at Sourceforge]
This Microsoft Windows 32 package distribution.exe
was generated from a C# program
and uses a boost_math.dll generated using the
Boost.Math C++ source code from the Boost.Math Toolkit, compiled in CLI mode,
containing the underlying statistical distribution classes and functions.
All source code is freely available for view and use under the
[@http://www.boost.org/LICENSE_1_0.txt Boost Open Source License].
[@https://svn.boost.org/svn/boost/sandbox\math_toolkit\libs\math\dot_net_example
Math Toolkit C++ source code]
to produce boost_math.dll is in the most recent [@http://www.boost.org Boost] release, initially 1.35.0.
It is distributed as a single Windows Installer package Setupdistex.msi.
Unzip the distexplorer.zip to a temporary location of your choice and run setup.exe.
(Note that .NET framework 2.0 and VCredist are requirements for this program.
Most recent and updated Windows environments will already have these,
but they are quickly, easily and safely installed from the Microsoft site if required.)
(The package cannot be run on other platforms at present but it should be possible
to build an equivalent utility on any C/C++ platform if anyone would like to undertake this task.)
[/ Distexplorer.qbk
Copyright 2008 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

216
doc/distexplorer/html/index.html Normal file
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@@ -0,0 +1,216 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Statistical Distribution Explorer</title>
<link rel="stylesheet" href="../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="index.html" title="Statistical Distribution Explorer">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
<td align="center"><a href="../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav"></div>
<div class="article" lang="en">
<div class="titlepage">
<div>
<div><h2 class="title">
<a name="statistical_distribution_explorer"></a>Statistical Distribution Explorer</h2></div>
<div><div class="authorgroup">
<div class="author"><h3 class="author">
<span class="firstname">Paul A.</span> <span class="surname">Bristow</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">John</span> <span class="surname">Maddock</span>
</h3></div>
</div></div>
<div><p class="copyright">Copyright © 2008 Paul A. Bristow, John Maddock</p></div>
<div><div class="legalnotice">
<a name="id770834"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></div>
</div>
<hr>
</div>
<p>
A Windows utility to show the properties of statistical distributions using parameters
provided interactively by the user.
</p>
<p>
The distributions provided are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
bernoulli
</li>
<li>
beta_distribution
</li>
<li>
binomial_distribution
</li>
<li>
cauchy
</li>
<li>
chi_squared
</li>
<li>
exponential
</li>
<li>
extreme_value
</li>
<li>
fisher_f
</li>
<li>
gamma_distribution
</li>
<li>
lognormal_distribution
</li>
<li>
negative_binomial_distribution
</li>
<li>
normal_distribution
</li>
<li>
pareto
</li>
<li>
poisson
</li>
<li>
rayleigh
</li>
<li>
students_t
</li>
<li>
triangular
</li>
<li>
uniform
</li>
<li>
weibull
</li>
</ul></div>
<p>
Properties of distributions computed are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
mean
</li>
<li>
mode
</li>
<li>
median
</li>
<li>
variance
</li>
<li>
standard deviation
</li>
<li>
coefficient of variation,
</li>
<li>
skewness
</li>
<li>
kurtosis
</li>
<li>
excess
</li>
<li>
range supported
</li>
</ul></div>
<p>
Calculated, from values provided, are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
probability density (or mass) function (PDF)
</li>
<li>
cumulative distribution function (CDF), and complement
</li>
<li>
Quantiles (percentiles) are calculated for typical risk (alpha) probabilities
(0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilities provided by
the user.
</li>
</ul></div>
<p>
Results can be saved to text files using Save or SaveAs. All the values on the
four tabs are output to the file chosen, and are tab separated to assist input
to other programs, for example, spreadsheets or text editors.
</p>
<p>
Note: Excel (for example), only shows 10 decimal digits, by default: to display
the maximum possible precision (abotu 15 decimal digits), it is necessary to
format all cells to display this precision. Although unusually accurate, not
all values computed by Distexplorer will be as accurate as this. Values shown
as NaN cannot be calculated from the value(s) given, most commonly because the
value input is outside the range for the distribution.
</p>
<p>
For more information, including downloads, see
</p>
<p>
<a href="http://distexplorer.sourceforge.net/" target="_top">Distexplorer at Sourceforge</a>
</p>
<p>
This Microsoft Windows 32 package distribution.exe was generated from a C# program
and uses a boost_math.dll generated using the Boost.Math C++ source code from
the Boost.Math Toolkit, compiled in CLI mode, containing the underlying statistical
distribution classes and functions.
</p>
<p>
All source code is freely available for view and use under the <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Boost
Open Source License</a>.
</p>
<p>
<a href="https://svn.boost.org/svn/boost/sandbox%5Cmath_toolkit%5Clibs%5Cmath%5Cdot_net_example" target="_top">Math
Toolkit C++ source code</a> to produce boost_math.dll is in the most recent
<a href="http://www.boost.org" target="_top">Boost</a> release, initially 1.35.0.
</p>
<p>
It is distributed as a single Windows Installer package Setupdistex.msi. Unzip
the distexplorer.zip to a temporary location of your choice and run setup.exe.
</p>
<p>
(Note that .NET framework 2.0 and VCredist are requirements for this program.
Most recent and updated Windows environments will already have these, but they
are quickly, easily and safely installed from the Microsoft site if required.)
</p>
<p>
(The package cannot be run on other platforms at present but it should be possible
to build an equivalent utility on any C/C++ platform if anyone would like to
undertake this task.)
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: February 26, 2009 at 17:08:18 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
<div class="spirit-nav"></div>
</body>
</html>

1
doc/gcd/Jamfile.v2
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@@ -62,7 +62,6 @@ boostbook standalone
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
<format>pdf:<xsl:param>draft.mode="no"
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/gcd/html
;

1
doc/octonion/Jamfile.v2
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@@ -62,7 +62,6 @@ boostbook standalone
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
<format>pdf:<xsl:param>draft.mode="no"
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/octonion/html
;

1
doc/quaternion/Jamfile.v2
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@@ -62,7 +62,6 @@ boostbook standalone
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
<format>pdf:<xsl:param>draft.mode="no"
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/quaternion/html
;

8
doc/sf_and_dist/Jamfile.v2
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@@ -36,7 +36,12 @@ boostbook standalone
<xsl:param>toc.max.depth=4
# How far down we go with TOC's
<xsl:param>generate.section.toc.level=10
# Index on type:
<xsl:param>index.on.type=1
#<xsl:param>root.filename="sf_dist_and_tools"
#<xsl:param>graphicsize.extension=1
#<xsl:param>use.extensions=1
# PDF Options:
# TOC Generation: this is needed for FOP-0.9 and later:
@@ -62,10 +67,9 @@ boostbook standalone
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>admon.graphics.path=$(images_location)/../../svg-admon/
<format>pdf:<xsl:param>draft.mode="no"
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/sf_and_dist/html
;
install pdf-install : standalone : <location>. <install-type>PDF ;

101
doc/sf_and_dist/building.qbk Normal file
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@@ -0,0 +1,101 @@
[section:building If and How to Build the Library and its Examples and Tests]
[h4 Building the Library]
The first thing you need to ask yourself is "Do I need to build anything at all?"
as the bulk of this library is header only: meaning you can use it just by
#including the necessary header(s). Refer to
[link math_toolkit.extern_c C99 and C++ TR1 C-style Functions]
for pros and cons of using
the TR1 components as opposed to the header only ones.
The ['only] time you ['need] to build the library is if you want to use the
`extern "C"` functions declared in `<boost/math/tr1.hpp>`. To build this
using Boost.Build, from a commandline boost-root directory issue a command like:
bjam toolset=gcc --with-math install
will do the job on Linux, while:
bjam toolset=msvc --with-math --build-type=complete stage
will work better on Windows (leaving libraries built
in sub-folder `/stage` below your Boost root directory).
Either way you should consult the
[@http://www.boost.org/doc/libs/release/more/getting_started/index.html
getting started guide] for more information.
You can also build the libraries from your favourite IDE or command line tool:
each `extern "C"` function declared in `<boost/math/tr1.hpp>` has its own
source file with the same name in `libs/math/src/tr1`. Just select the
sources corresponding to the functions you are using and build them into
a library, or else add them directly to your project. Note that the
directory `libs/math/src/tr1` will need to be in your compiler's
#include path as well as the boost-root directory
(MSVC Tools, Options, Projects and Solutions, VC++ Directories, Include files).
[note If you are using
a Windows compiler that supports auto-linking and you have built the sources
yourself (or added them directly to your project) then you will need to
prevent `<boost/math/tr1.hpp>` from trying to auto-link to the binaries
that Boost.Build generates. You can do this by defining either
BOOST_MATH_NO_LIB or BOOST_ALL_NO_LIB at project level
(so the defines get passed to each compiler invocation).
]
Optionally the sources in `libs/math/src/tr1` have support for using
`libs/math/src/tr1/pch.hpp` as a precompiled header
['if your compiler supports precompiled headers.] Note that normally
this header is a do-nothing include: to activate the header so that
it #includes everything required by all the sources you will need to
define BOOST_BUILD_PCH_ENABLED on the command line, both when building
the pre-compiled header and when building the sources. Boost.Build
will do this automatically when appropriate.
[h4 Building the Examples]
The examples are all located in `libs/math/example`, they can all
be built without reference to any external libraries, either with
Boost.Build using the supplied Jamfile, or from your compiler's
command line. The only requirement is that the Boost headers are
in your compilers #include search path.
[h4 Building the Tests]
The tests are located in `libs/math/test` and are best built
using Boost.Build and the supplied Jamfile. If you plan to
build them separately from your favourite IDE then you will
need to add `libs/math/test` to the list of your compiler's
search paths.
You will also need to build and link to
the Boost.Regex library for many of the tests: this can built
from the command line by following the
[@http://www.boost.org/doc/libs/release/more/getting_started/index.html
getting started guide], using a command such as:
bjam toolset=gcc --with-regex install
or
bjam toolset=msvc --with-regex --build-type=complete stage
depending on whether you are on Linux or Windows.
Many of the tests have optional precompiled header support
using the header `libs/math/test/pch.hpp`.
Note that normally
this header is a do-nothing include: to activate the header so that
it #includes everything required by all the sources you will need to
define BOOST_BUILD_PCH_ENABLED on the command line, both when building
the pre-compiled header and when building the sources. Boost.Build
will do this automatically when appropriate.
[endsect]
[/ building.qbk
Copyright 2006, 2007, 2008 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

2
doc/sf_and_dist/c99_ref.qbk
View File

@@ -286,6 +286,8 @@ Returns /x/ truncated to the nearest integer.
See also __trunc for the full template (header only) version of this function.
See also [@http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1124.pdf C99 ISO Standard]
[endsect]
[/

2
doc/sf_and_dist/common_overviews.qbk
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@@ -61,7 +61,7 @@ of breed" algorithms as many other libraries: the principle difference
is that this library is implemented in C++ - taking advantage of all
the abstraction mechanisms that C++ offers - where as most traditional
numeric libraries are implemented in C or FORTRAN. Traditionally
languages such as C or FORTAN are perceived as easier to optimise
languages such as C or FORTRAN are perceived as easier to optimise
than more complex languages like C++, so in a sense this library
provides a good test of current compiler technology, and the
"abstraction penalty" - if any - of C++ compared to other languages.

57
doc/sf_and_dist/concepts.qbk
View File

@@ -14,17 +14,58 @@ replacement for the "real" NTL::RR that adds some syntactic sugar to keep
this library happy, plus some of the standard library functions not implemented
in NTL.
Finally there is a high precision __lanczos suitable for use with `boost::math::ntl::RR`,
used at 1000-bit precision in
[@../../../tools/ntl_rr_lanczos.hpp libs/math/tools/ntl_rr_lanczos.hpp].
The approximation has a theoretical precision of > 90 decimal digits,
and an experimental precision of > 100 decimal digits. To use that
approximation, just include that header before any of the special
function headers (if you don't use it, you'll get a slower, but
fully generic implementation for all of the gamma-like functions).
For those functions that are based upon the __lanczos, the bindings
defines a series of approximations with up to 61 terms and accuracy
up to approximately 3e-113. This therefore sets the upper limit for accuracy
to the majority of functions defined this library when used with `NTL::RR`.
There is a concept checking test program for NTL support
[@../../../../../libs/math/test/ntl_concept_check.cpp here].
[endsect][/section:use_ntl Using With NTL - a High Precision Floating-Point Library]
[section:use_mpfr Using With MPFR / GMP - a High-Precision Floating-Point Library]
The special functions and tools in this library can be used with
[@http://www.mpfr.org MPFR (an arbitrary precision number type based on the GMP library)],
via the bindings in [@../../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp].
In order to use these binings you will need to have installed [@http://www.mpfr.org MPFR]
plus it's dependency the [@http://gmplib.org GMP library] and the C++ wrapper for MPFR known as
[@http://math.berkeley.edu/~wilken/code/gmpfrxx/ gmpfrxx (or mpfr_class)].
Unfortunately `mpfr_class` doesn't quite satisfy our conceptual requirements,
so there is a very thin set of additional interfaces and some helper traits defined in
[@../../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp] that you
should use in place of including 'gmpfrxx.h' directly. The existing mpfr_class is
then usable unchanged once this header is included, so it's performance-enhancing
expression templates are preserved and fully supported by this library:
#include <boost/math/bindings/mpfr.hpp>
#include <boost/math/special_functions/gamma.hpp>
int main()
{
mpfr_class::set_dprec(500); // 500 bit precision
//
// Note that the argument to tgamma is an expression template,
// that's just fine here:
//
mpfr_class v = boost::math::tgamma(sqrt(mpfr_class(2)));
std::cout << std::setprecision(50) << v << std::endl;
}
For those functions that are based upon the __lanczos, the bindings
defines a series of approximations with up to 61 terms and accuracy
up to approximately 3e-113. This therefore sets the upper limit for accuracy
to the majority of functions defined this library when used with `mpfr_class`.
There is a concept checking test program for mpfr support
[@../../../../../libs/math/test/mpfr_concept_check.cpp here].
[endsect][/section:use_mpfr Using With MPFR / GMP - a High-Precision Floating-Point Library]
[section:concepts Conceptual Requirements for Real Number Types]
The functions, and statistical distributions in this library can be used with

32
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@@ -7,13 +7,13 @@ John Maddock started this library, the beta, gamma, erf, polynomial,
and factorial functions are his, as is the "Toolkit" section, and many
of the statistical distributions.
Paul A. Bristow threw down the challenge in
[@http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf
A Proposal to add Mathematical Functions for Statistics to the C++
Paul A. Bristow threw down the challenge in
[@http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf
A Proposal to add Mathematical Functions for Statistics to the C++
Standard Library] to add the key math functions, especially those essential for
statistics. After JM accepted and solved the difficult problems,
statistics. After JM accepted and solved the difficult problems,
not only numerically, but in full C++ template style, PAB
implemented a few of the statistical distributions. PAB also tirelessly
implemented a few of the statistical distributions. PAB also tirelessly
proof-read everything that JM threw at him (so that all
remaining editorial mistakes are his fault).
@@ -25,16 +25,20 @@ Bruno Lalande submitted the "compile time power of a runtime base" code.
Johan R'''&#xE5;'''de wrote the optimised floating point classification
code.
Gautam Sewani coded the logistic distribution as part of a Google Summer of Code project 2008.
M. A. (Thijs) van den Berg coded the Laplace distribution.
(Thijs has also threatened to implement some multivariate distributions).
Professor Nico Temme for advice on the inverse incomplete beta function.
[@http://www.shoup.net Victor Shoup for NTL],
without which it would have much difficult to
[@http://www.shoup.net Victor Shoup for NTL],
without which it would have much more difficult to
produce high accuracy constants, and especially
the tables of accurate values for testing.
We are grateful to Joel Guzman for helping us stress-test
his
[@http://www.boost.org/tools/quickbook/index.htm Boost.Quickbook]
We are grateful to Joel Guzman for helping us stress-test his
[@http://www.boost.org/tools/quickbook/index.htm Boost.Quickbook]
program used to generate the html and pdf versions
of this document, adding several new features en route.
@@ -48,17 +52,17 @@ Since browser support for rendering SVG is still not universal
but can be made to work with
[@http://www.adobe.com/svg/viewer/install/ Adobe's free SVG viewer] plugin),
so the SVG files were batch converted to JPEG using
[@http://www.inkscape.org/ Inkscape].
[@http://www.inkscape.org/ Inkscape].
We are also indebted to Matthias Schabel for managing the formal Boost-review
of this library, and to all the reviewers - including Guillaume Melquiond,
Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland
Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland
- for their many helpful comments.
[endsect] [/section:credits Credits and Acknowledgements]
[/
Copyright 2006, 2007, 2008 John Maddock and Paul A. Bristow.
[/
Copyright 2006, 2007, 2008, 2009 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).

3
doc/sf_and_dist/dist_reference.qbk
View File

@@ -13,6 +13,9 @@
[include distributions/extreme_value.qbk]
[include distributions/fisher.qbk]
[include distributions/gamma.qbk]
[include distributions/hypergeometric.qbk]
[include distributions/laplace.qbk]
[include distributions/logistic.qbk]
[include distributions/lognormal.qbk]
[include distributions/negative_binomial.qbk]
[include distributions/nc_beta.qbk]

153
doc/sf_and_dist/dist_tutorial.qbk
View File

@@ -5,17 +5,17 @@
[def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]]
[def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]]
[def __handbook [@http://www.itl.nist.gov/div898/handbook/
[def __handbook [@http://www.itl.nist.gov/div898/handbook/
NIST/SEMATECH e-Handbook of Statistical Methods.]]
[section:stat_tut Statistical Distributions Tutorial]
This library is centred around statistical distributions, this tutorial
will give you an overview of what they are, how they can be used, and
will give you an overview of what they are, how they can be used, and
provides a few worked examples of applying the library to statistical tests.
[section:overview Overview]
[section:overview Overview of Distributions]
[h4 Headers and Namespaces]
[section:headers Headers and Namespaces]
All the code in this library is inside namespace boost::math.
@@ -27,27 +27,29 @@ For example, to use the Students-t distribution include either
<boost/math/distributions/students_t.hpp> or
<boost/math/distributions.hpp>
[h4 Distributions are Objects]
[endsect] [/ section:headers Headers and Namespaces]
Each kind of distribution in this library is a class type.
[section:objects Distributions are Objects]
[link math_toolkit.policy Policies] provide fine-grained control
Each kind of distribution in this library is a class type - an object.
[link math_toolkit.policy Policies] provide fine-grained control
of the behaviour of these classes, allowing the user to customise
behaviour such as how errors are handled, or how the quantiles
of discrete distribtions behave.
[tip If you are familiar with statistics libraries using functions,
and 'Distributions as Objects' seem alien, see
[link math_toolkit.dist.stat_tut.weg.nag_library the comparison to
other statistics libraries.]
[link math_toolkit.dist.stat_tut.weg.nag_library the comparison to
other statistics libraries.]
] [/tip]
Making distributions class types does two things:
* It encapsulates the kind of distribution in the C++ type system;
so, for example, Students-t distributions are always a different C++ type from
* It encapsulates the kind of distribution in the C++ type system;
so, for example, Students-t distributions are always a different C++ type from
Chi-Squared distributions.
* The distribution objects store any parameters associated with the
* The distribution objects store any parameters associated with the
distribution: for example, the Students-t distribution has a
['degrees of freedom] parameter that controls the shape of the distribution.
This ['degrees of freedom] parameter has to be provided
@@ -57,60 +59,63 @@ Although the distribution classes in this library are templates, there
are typedefs on type /double/ that mostly take the usual name of the
distribution
(except where there is a clash with a function of the same name: beta and gamma,
in which case using the default template arguments - `RealType = double` -
in which case using the default template arguments - `RealType = double` -
is nearly as convenient).
Probably 95% of uses are covered by these typedefs:
using namespace boost::math;
// Construct a students_t distribution with 4 degrees of freedom:
students_t d1(4);
// Construct a double-precision beta distribution
// Construct a double-precision beta distribution
// with parameters a = 10, b = 20
beta_distribution<> d2(10, 20); // Note: _distribution<> suffix !
If you need to use the distributions with a type other than `double`,
then you can instantiate the template directly: the names of the
then you can instantiate the template directly: the names of the
templates are the same as the `double` typedef but with `_distribution`
appended, for example: __students_t_distrib or __binomial_distrib:
// Construct a students_t distribution, of float type,
// with 4 degrees of freedom:
students_t_distribution<float> d3(4);
// Construct a binomial distribution, of long double type,
// with probability of success 0.3
// and 20 trials in total:
binomial_distribution<long double> d4(20, 0.3);
The parameters passed to the distributions can be accessed via getter member
functions:
d1.degrees_of_freedom(); // returns 4.0
d1.degrees_of_freedom(); // returns 4.0
This is all well and good, but not very useful so far. What we often want
is to be able to calculate the /cumulative distribution functions/ and
/quantiles/ etc for these distributions.
[h4 Generic operations common to all distributions are non-member functions]
[endsect] [/section:objects Distributions are Objects]
[section:generic Generic operations common to all distributions are non-member functions]
Want to calculate the PDF (Probability Density Function) of a distribution?
No problem, just use:
pdf(my_dist, x); // Returns PDF (density) at point x of distribution my_dist.
Or how about the CDF (Cumulative Distribution Function):
cdf(my_dist, x); // Returns CDF (integral from -infinity to point x)
// of distribution my_dist.
And quantiles are just the same:
quantile(my_dist, p); // Returns the value of the random variable x
// such that cdf(my_dist, x) == p.
If you're wondering why these aren't member functions, it's to
If you're wondering why these aren't member functions, it's to
make the library more easily extensible: if you want to add additional
generic operations - let's say the /n'th moment/ - then all you have to
do is add the appropriate non-member functions, overloaded for each
@@ -124,9 +129,9 @@ If you want random numbers that are distributed in a specific way,
for example in a uniform, normal or triangular,
see [@http://www.boost.org/libs/random/ Boost.Random].
Whilst in principal there's nothing to prevent you from using the
Whilst in principal there's nothing to prevent you from using the
quantile function to convert a uniformly distributed random
number to another distribution, in practice there are much more
number to another distribution, in practice there are much more
efficient algorithms available that are specific to random number generation.
] [/tip Random numbers that approximate Quantiles of Distributions]
@@ -136,7 +141,7 @@ n (the number of trials) and p (the probability of success on one trial).
The `binomial_distribution` constructor therefore has two parameters:
`binomial_distribution(RealType n, RealType p);`
For this distribution the random variate is k: the number of successes observed.
The probability density\/mass function (pdf) is therefore written as ['f(k; n, p)].
@@ -153,15 +158,15 @@ to separate the variate from the parameter(s) that defines the shape of the dist
] [/tip Random Variates and Distribution Parameters]
As noted above the non-member function `pdf` has one parameter for the distribution object,
and a second for the random variate. So taking our binomial distribution
and a second for the random variate. So taking our binomial distribution
example, we would write:
`pdf(binomial_distribution<RealType>(n, p), k);`
The ranges of random variate values that are permitted and are supported can be
The ranges of random variate values that are permitted and are supported can be
tested by using two functions `range` and `support`.
The distribution (effectively the random variate) is said to be 'supported'
The distribution (effectively the random variate) is said to be 'supported'
over a range that is
[@http://en.wikipedia.org/wiki/Probability_distribution
"the smallest closed set whose complement has probability zero"].
@@ -180,15 +185,15 @@ If you are plotting the PDF, or otherwise calculating,
zero is not the most useful value for the lower limit of supported, as we discovered.
So for this, and similar distributions,
we have decided it is most numerically useful to use
the closest value to zero, min_value, for the limit of the supported range.
the closest value to zero, min_value, for the limit of the supported range.
(The `range` remains from zero, so you will still get `pdf(weibull, 0) == 0`).
(Exponential and gamma distributions have similarly discontinuous functions).
Mathematically, the functions may make sense with an (+ or -) infinite value,
but except for a few special cases (in the Normal and Cauchy distributions)
this implementation limits random variates to finite values from the `max`
this implementation limits random variates to finite values from the `max`
to `min` for the `RealType`.
(See [link math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity
(See [link math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity
Handling of Floating-Point Infinity] for rationale).
@@ -196,23 +201,23 @@ Handling of Floating-Point Infinity] for rationale).
[*Discrete Probability Distributions]
Note that the [@http://en.wikipedia.org/wiki/Discrete_probability_distribution
Note that the [@http://en.wikipedia.org/wiki/Discrete_probability_distribution
discrete distributions], including the binomial, negative binomial, Poisson & Bernoulli,
are all mathematically defined as discrete functions:
that is to say the functions `cdf` and `pdf` are only defined for integral values
that is to say the functions `cdf` and `pdf` are only defined for integral values
of the random variate.
However, because the method of calculation often uses continuous functions
it is convenient to treat them as if they were continuous functions,
and permit non-integral values of their parameters.
Users wanting to enforce a strict mathematical model may use `floor`
or `ceil` functions on the random variate prior to calling the distribution
Users wanting to enforce a strict mathematical model may use `floor`
or `ceil` functions on the random variate prior to calling the distribution
function.
The quantile functions for these distributions are hard to specify
in a manner that will satisfy everyone all of the time. The default
behaviour is to return an integer result, that has been rounded
behaviour is to return an integer result, that has been rounded
/outwards/: that is to say, lower quantiles - where the probablity
is less than 0.5 are rounded down, while upper quantiles - where
the probability is greater than 0.5 - are rounded up. This behaviour
@@ -221,17 +226,17 @@ coverage will be present in the central region, and /no more than/
the requested coverage will be present in the tails.
This behaviour can be changed so that the quantile functions are rounded
differently, or return a real-valued result using
differently, or return a real-valued result using
[link math_toolkit.policy.pol_overview Policies]. It is strongly
recommended that you read the tutorial
recommended that you read the tutorial
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on a discrete distribtion. The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
describe how to change the rounding policy
for these distributions.
For similar reasons continuous distributions with parameters like
For similar reasons continuous distributions with parameters like
"degrees of freedom"
that might appear to be integral, are treated as real values
(and are promoted from integer to floating-point if necessary).
@@ -239,16 +244,17 @@ In this case however, there are a small number of situations where non-integral
degrees of freedom do have a genuine meaning.
]
[endsect] [/ section:generic Generic operations common to all distributions are non-member functions]
[#complements]
[h4 Complements are supported too]
[section:complements Complements are supported too - and when to use them]
Often you don't want the value of the CDF, but its complement, which is
to say `1-p` rather than `p`. You could calculate the CDF and subtract
to say `1-p` rather than `p`. It is tempting to calculate the CDF and subtract
it from `1`, but if `p` is very close to `1` then cancellation error
will cause you to lose significant digits. In extreme cases, `p` may
actually be equal to `1`, even though the true value of the complement is non-zero.
will cause you to lose accuracy, perhaps totally.
[link why_complements See also ['"Why complements?"]]
[link why_complements See below ['"Why and when to use complements?"]]
In this library, whenever you want to receive a complement, just wrap
all the function arguments in a call to `complement(...)`, for example:
@@ -262,7 +268,7 @@ Any function that accepts a probability as an argument can also accept a complem
by wrapping all of its arguments in a call to `complement(...)`, for example:
students_t dist(5);
for(double i = 10; i < 1e10; i *= 10)
{
// Calculate the quantile for a 1 in i chance:
@@ -271,12 +277,12 @@ by wrapping all of its arguments in a call to `complement(...)`, for example:
cout << "Quantile of students-t with 5 degrees of freedom\n"
"for a 1 in " << i << " chance is " << t << endl;
}
[tip
[*Critical values are just quantiles]
Some texts talk about quantiles, others about critical values, the basic rule is:
Some texts talk about quantiles, or percentiles, others about critical values, the basic rule is:
['Lower critical values] are the same as the quantile.
@@ -284,7 +290,7 @@ Some texts talk about quantiles, others about critical values, the basic rule is
of the probability.
For example, suppose we have a Bernoulli process, giving rise to a binomial
distribution with success ratio 0.1 and 100 trials in total. The
distribution with success ratio 0.1 and 100 trials in total. The
['lower critical value] for a probability of 0.05 is given by:
`quantile(binomial(100, 0.1), 0.05)`
@@ -311,7 +317,7 @@ bit that didn't cancel out!
Or to look at this another way: consider that we want the risk of falsely
rejecting the null-hypothesis in the Student's t test to be 1 in 1 billion,
for a sample size of 10,000.
This gives a probability of 1 - 10[super -9], which is exactly 1 when
This gives a probability of 1 - 10[super -9], which is exactly 1 when
calculated at float precision. In this case calculating the quantile from
the complement neatly solves the problem, so for example:
@@ -326,11 +332,32 @@ raises an overflow error, since it is the same as:
`quantile(students_t(10000), 1)`
Which has no finite result.
]
[h4 Parameters can be calculated]
With all distributions, even for more reasonable probability
(unless the value of p can be represented exactly in the floating-point type)
the loss of accuracy quickly becomes significant if you simply calculate probability from 1 - p
(because it will be mostly garbage digits for p ~ 1).
Sometimes it's the parameters that define the distribution that you
So always avoid, for example, using a probability near to unity like 0.99999
`quantile(my_distribution, 0.99999)`
and instead use
`quantile(complement(my_distribution, 0.00001))`
since 1 - 0.99999 is not exactly equal to 0.00001 when using floating-point arithmetic.
This assumes that the 0.00001 value is either a constant,
or can be computed by some manner other than subtracting 0.99999 from 1.
] [/ tip *Why bother with complements anyway?]
[endsect] [/ section:complements Complements are supported too - and why]
[section:parameters Parameters can be calculated]
Sometimes it's the parameters that define the distribution that you
need to find. Suppose, for example, you have conducted a Students-t test
for equal means and the result is borderline. Maybe your two samples
differ from each other, or maybe they don't; based on the result
@@ -346,7 +373,7 @@ of the distributions, for example:
0.05, // maximum risk of falsely rejecting the null-hypothesis.
0.1, // maximum risk of falsely failing to reject the null-hypothesis.
0.13); // sample standard deviation
Returns the number of degrees of freedom required to obtain a 95%
probability that the observed differences in means is not down to
chance alone. In the case that a borderline Students-t test result
@@ -354,8 +381,10 @@ was previously obtained, this can be used to estimate how large the sample size
would have to become before the observed difference was considered
significant. It assumes, of course, that the sample mean and standard
deviation are invariant with sample size.
[h4 Summary]
[endsect] [/ section:parameters Parameters can be calculated]
[section:summary Summary]
* Distributions are objects, which are constructed from whatever
parameters the distribution may have.
@@ -372,6 +401,7 @@ to be found from other information.
Now that you have the basics, the next section looks at some worked examples.
[endsect] [/section:summary Summary]
[endsect] [/section:overview Overview]
[section:weg Worked Examples]
@@ -386,6 +416,7 @@ Now that you have the basics, the next section looks at some worked examples.
[include distributions/error_handling_example.qbk]
[include distributions/find_location_and_scale.qbk]
[include distributions/nag_library.qbk]
[include distributions/c_sharp.qbk]
[endsect] [/section:weg Worked Examples]
[include background.qbk]

20
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@@ -0,0 +1,20 @@
[section:c_sharp Using the Distributions from Within C#]
The distributions in this library can be used from the C# programming language
when they are built using Microsofts Common Language Runtime option.
An example of this kind of usage is given in the
[@../../distexplorer/html/index.html distribution_explorer] example:
see =boost-root/libs/math/dot_net_example=
for the source code: the application consists of a C++ dll that contains the
actual distributions, and a C# GUI that allows you to explore their properties.
[endsect] [/section:c_sharp]
[/
Copyright 2006 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

229
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@@ -0,0 +1,229 @@
[section:hypergeometric_dist Hypergeometric Distribution]
``#include <boost/math/distributions/hypergeometric.hpp>``
namespace boost{ namespace math{
template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class hypergeometric_distribution;
template <class RealType, class Policy>
class hypergeometric_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
// Construct:
hypergeometric_distribution(unsigned r, unsigned n, unsigned N);
// Accessors:
unsigned total()const;
unsigned defective()const;
unsigned sample_count()const;
};
typedef hypergeometric_distribution<> hypergeometric;
}} // namespaces
The hypergeometric distribution describes the number of "events" /k/
from a sample /n/ drawn from a total population /N/ ['without replacement].
Imagine we have a sample of /N/ objects of which /r/ are "defective"
and N-r are "not defective"
(the terms "success\/failure" or "red\/blue" are also used). If we sample /n/
items /without replacement/ then what is the probability that exactly
/k/ items in the sample are defective? The answer is given by the pdf of the
hypergeometric distribution `f(k; r, n, N)`, whilst the probability of
/k/ defectives or fewer is given by F(k; r, n, N), where F(k) is the
CDF of the hypergeometric distribution.
[note Unlike almost all of the other distributions in this library,
the hypergeometric distribution is strictly discrete: it can not be
extended to real valued arguments of its parameters or random variable.]
The following graph shows how the distribution changes as the proportion
of "defective" items changes, while keeping the population and sample sizes
constant:
[graph hypergeometric_pdf_1]
Note that since the distribution is symmetrical in parameters /n/ and /r/, if we
change the sample size and keep the population and proportion "defective" the same
then we obtain basically the same graphs:
[graph hypergeometric_pdf_2]
[h4 Member Functions]
hypergeometric_distribution(unsigned r, unsigned n, unsigned N);
Constructs a hypergeometric distribution with with a population of /N/ objects,
of which /r/ are defective, and from which /n/ are sampled.
unsigned total()const;
Returns the total number of objects /N/.
unsigned defective()const;
Returns the number of objects /r/ in population /N/ which are defective.
unsigned sample_count()const;
Returns the number of objects /n/ which are sampled from the population /N/.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is the unsigned integers in the range
\[max(0, n + r - N), min(n, r)\]. A __domain_error is raised if the
random variable is outside this range, or is not an integral value.
[caution
The quantile function will by default return an integer result that has been
/rounded outwards/. That is to say lower quantiles (where the probability is
less than 0.5) are rounded downward, and upper quantiles (where the probability
is greater than 0.5) are rounded upwards. This behaviour
ensures that if an X% quantile is requested, then /at least/ the requested
coverage will be present in the central region, and /no more than/
the requested coverage will be present in the tails.
This behaviour can be changed so that the quantile functions are rounded
differently using
[link math_toolkit.policy.pol_overview Policies]. It is strongly
recommended that you read the tutorial
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on the Hypergeometric distribution. The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
describe how to change the rounding policy
for these distributions.
However, note that the implementation method of the quantile function
always returns an integral value, therefore attempting to use a __Policy
that requires (or produces) a real valued result will result in a
compile time error.
] [/ caution]
[h4 Accuracy]
For small N such that
`N < boost::math::max_factorial<RealType>::value` then table based
lookup of the results gives an accuracy to a few epsilon.
`boost::math::max_factorial<RealType>::value` is 170 at double or long double
precision.
For larger N such that `N < boost::math::prime(boost::math::max_prime)`
then only basic arithmetic is required for the calculation
and the accuracy is typically < 20 epsilon. This takes care of N
up to 104729.
For `N > boost::math::prime(boost::math::max_prime)` then accuracy quickly
degrades, with 5 or 6 decimal digits being lost for N = 110000.
In general for very large N, the user should expect to loose log[sub 10]N
decimal digits of precision during the calculation, with the results
becoming meaningless for N >= 10[super 15].
[h4 Testing]
There are three sets of tests: our implementation is tested against a table of values
produced by Mathematica's implementation of this distribution. We also sanity check
our implementation against some spot values computed using the online calculator
here [@http://stattrek.com/Tables/Hypergeometric.aspx http://stattrek.com/Tables/Hypergeometric.aspx].
Finally we test accuracy against some high precision test data using
this implementation and NTL::RR.
[h4 Implementation]
The PDF can be calculated directly using the formula:
[equation hypergeometric1]
However, this can only be used directly when the largest of the factorials
is guaranteed not to overflow the floating point representation used.
This formula is used directly when `N < max_factorial<RealType>::value`
in which case table lookup of the factorials gives a rapid and accurate
implementation method.
For larger /N/ the method described in
"An Accurate Computation of the Hypergeometric Distribution Function",
Trong Wu, ACM Transactions on Mathematical Software, Vol. 19, No. 1,
March 1993, Pages 33-43 is used. The method relies on the fact that
there is an easy method for factorising a factorial into the product
of prime numbers:
[equation hypergeometric2]
Where p[sub i] is the i'th prime number, and e[sub i] is a small
positive integer or zero, which can be calculated via:
[equation hypergeometric3]
Further we can combine the factorials in the expression for the PDF
to yield the PDF directly as the product of prime numbers:
[equation hypergeometric4]
With this time the exponents e[sub i] being either positive, negative
or zero. Indeed such a degree of cancellation occurs in the calculation
of the e[sub i] that many are zero, and typically most have a magnitude
or no more than 1 or 2.
Calculation of the product of the primes requires some care to prevent
numerical overflow, we use a novel recursive method which splits the
calculation into a series of sub-products, with a new sub-product
started each time the next multiplication would cause either overflow
or underflow. The sub-products are stored in a linked list on the
program stack, and combined in an order that will guarantee no overflow
or unnecessary-underflow once the last sub-product has been calculated.
This method can be used as long as N is smaller than the largest prime
number we have stored in our table of primes (currently 104729). The method
is relatively slow (calculating the exponents requires the most time), but
requires only a small number of arithmetic operations to
calculate the result (indeed there is no shorter method involving only basic
arithmetic once the exponents have been found), the method is therefore
much more accurate than the alternatives.
For much larger N, we can calculate the PDF from the factorials using
either lgamma, or by directly combining lanczos approximations to avoid
calculating via logarithms. We use the latter method, as it is usually
1 or 2 decimal digits more accurate than computing via logarithms with
lgamma. However, in this area where N > 104729, the user should expect
to loose around log[sub 10]N decimal digits during the calculation in
the worst case.
The CDF and its complement is calculated by directly summing the PDF's.
We start by deciding whether the CDF, or its complement, is likely to be
the smaller of the two and then calculate the PDF at /k/ (or /k+1/ if we're
calculating the complement) and calculate successive PDF values via the
recurrence relations:
[equation hypergeometric5]
Until we either reach the end of the distributions domain, or the next
PDF value to be summed would be too small to affect the result.
The quantile is calculated in a similar manner to the CDF: we first guess
which end of the distribution we're nearer to, and then sum PDFs starting
from the end of the distribution this time, until we have some value /k/ that
gives the required CDF.
The median is simply the quantile at 0.5, and the remaining properties are
calculated via:
[equation hypergeometric6]
[endsect]
[/ hypergeometric.qbk
Copyright 2008 John Maddock.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

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@@ -0,0 +1,145 @@
[section:laplace_dist Laplace Distribution]
``#include <boost/math/distributions/laplace.hpp>``
namespace boost{ namespace math{
template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class laplace_distribution;
typedef laplace_distribution<> laplace;
template <class RealType, class ``__Policy``>
class laplace_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
// Construct:
laplace_distribution(RealType location = 0, RealType scale = 1);
// Accessors:
RealType location()const;
RealType scale()const;
};
}} // namespaces
Laplace distribution is the distribution of differences between two independent variates
with identical exponential distributions (Abramowitz and Stegun 1972, p. 930).
It is also called the double exponential distribution.
[/ Wikipedia definition is The difference between two independent identically distributed
exponential random variables is governed by a Laplace distribution.]
For location parameter [mu][space] and scale parameter [sigma][space] it is defined by the
probability density function:
[equation laplace_pdf]
The location and scale parameters are equivalent to the mean and
standard deviation of the normal or Gaussian distribution.
The following graph illustrates the effect of the location
parameter [mu][space] on the PDF. Note that the range of the random
variable remains \[-[infin],+[infin]\] irrespective of the value of the
location parameter:
[graph laplace_pdf_mu]
The next graph illustrates the effect of the scale parameter [sigma][space] on the PDF:
[graph laplace_pdf_sigma]
[h4 Member Functions]
laplace_distribution(RealType location = 0, RealType scale = 1);
Constructs a laplace distribution with location /location/ and
scale /scale/.
The location parameter is the same as the mean of the random variate.
The scale parameter is proportional to the standard deviation of the random variate.
Requires that the scale parameter is greater than zero, otherwise calls
__domain_error.
RealType location()const;
Returns the /location/ parameter of this distribution.
RealType scale()const;
Returns the /scale/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[-[infin],+[infin]\].
[h4 Accuracy]
The laplace distribution is implemented in terms of the
standard library log and exp functions and as such should have very small errors.
[h4 Implementation]
In the following table [mu] is the location parameter of the distribution,
[sigma] is its scale parameter, /x/ is the random variate, /p/ is the probability
and its complement /q = 1-p/.
[table
[[Function][Implementation Notes]]
[[pdf][Using the relation: pdf = e[super -abs(x-[mu]) \/ [sigma]] \/ (2 * [sigma]) ]]
[[cdf][Using the relations:
x < [mu] : p = e[super (x-[mu])/[sigma] ] \/ [sigma]
x >= [mu] : p = 1 - e[super ([mu]-x)/[sigma] ] \/ [sigma]
]]
[[cdf complement][Using the relation:
-x < [mu] : q = e[super (-x-[mu])/[sigma] ] \/ [sigma]
-x >= [mu] : q = 1 - e[super ([mu]+x)/[sigma] ] \/ [sigma]
]]
[[quantile][Using the relations:
p < 0.5 : x = [mu] + [sigma] * log(2*p)
p >= 0.5 : x = [mu] - [sigma] * log(2-2*p)
]]
[[quantile from the complement][Using the relation:
q > 0.5: x = [mu] + [sigma]*log(2-2*q)
q <=0.5: x = [mu] - [sigma]*log( 2*q )
]]
[[mean][[mu]]]
[[variance][2 * [sigma][super 2] ]]
[[mode][[mu]]]
[[skewness][0]]
[[kurtosis][6]]
[[kurtosis excess][3]]
]
[h4 References]
* [@http://mathworld.wolfram.com/LaplaceDistribution.html Weisstein, Eric W. "Laplace Distribution."] From MathWorld--A Wolfram Web Resource.
* [@http://en.wikipedia.org/wiki/Laplace_distribution Laplace Distribution]
* M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, p. 930.
[endsect][/section:laplace_dist laplace]
[/
Copyright 2008, 2009 John Maddock, Paul A. Bristow and M.A. (Thijs) van den Berg.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

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@@ -0,0 +1,103 @@
[section:logistic_dist Logistic Distribution]
``#include <boost/math/distributions/logistic.hpp>``
namespace boost{ namespace math{
template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class logistic_distribution;
template <class RealType, class Policy>
class logistic_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
// Construct:
logistic_distribution(RealType location = 0, RealType scale = 1);
// Accessors:
RealType location()const; // location.
RealType scale()const; // scale.
};
typedef logistic_distribution<> logistic;
}} // namespaces
The logistic distribution is a continous probability distribution.
It has two parameters - location and scale. The cumulative distribution
function of the logistic distribution appears in logistic regression
and feedforward neural networks. Among other applications,
United State Chess Federation and FIDE use it to calculate chess ratings.
The following graph shows how the distribution changes as the
parameters change:
[graph logistic_pdf]
[h4 Member Functions]
logistic_distribution(RealType u = 0, RealType s = 1);
Constructs a logistic distribution with location /u/ and scale /s/.
Requires `scale > 0`, otherwise a __domain_error is raised.
RealType location()const;
Returns the location of this distribution.
RealType scale()const;
Returns the scale of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[-\[max_value\], +\[min_value\]\].
However, the pdf and cdf support inputs of +[infin] and -[infin]
as special cases if RealType permits.
At `p=1` and `p=0`, the quantile function returns the result of
+__overflow_error and -__overflow_error, while the complement
quantile function returns the result of -__overflow_error and
+__overflow_error respectively.
[h4 Accuracy]
The logistic distribution is implemented in terms of the `std::exp`
and the `std::log` functions, so its accuracy is related to the
accurate implementations of those functions on a given platform.
When calculating the quantile with a non-zero /position/ parameter
catastrophic cancellation errors can occur:
in such cases, only a low /absolute error/ can be guarenteed.
[h4 Implementation]
[table
[[Function][Implementation Notes]]
[[pdf][Using the relation: pdf = e[super -(x-u)/s] / (s*(1+e[super -(x-u)/s])[super 2])]]
[[cdf][Using the relation: p = 1/(1+e[super -(x-u)/s])]]
[[cdf complement][Using the relation: q = 1/(1+e[super (x-u)/s])]]
[[quantile][Using the relation: x = u - s*log(1/p-1)]]
[[quantile from the complement][Using the relation: x = u + s*log(p/1-p)]]
[[mean][u]]
[[mode][The same as the mean.]]
[[skewness][0]]
[[kurtosis excess][6/5]]
[[variance][ ([pi]*s)[super 2] / 3]]
]
[endsect]
[/ logistic.qbk
Copyright 2006, 2007 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).
]

74
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@@ -3,41 +3,42 @@
``#include <boost/math/distributions/pareto.hpp>``
namespace boost{ namespace math{
template <class RealType = double,
namespace boost{ namespace math{
template <class RealType = double,
class ``__Policy`` = ``__policy_class`` >
class pareto_distribution;
typedef pareto_distribution<> pareto;
template <class RealType, class ``__Policy``>
class pareto_distribution
{
public:
typedef RealType value_type;
// Constructor:
pareto_distribution(RealType location = 1, RealType shape = 1)
pareto_distribution(RealType scale = 1, RealType shape = 1)
// Accessors:
RealType location()const;
RealType scale()const;
RealType shape()const;
};
}} // namespaces
The [@http://en.wikipedia.org/wiki/pareto_distribution Pareto distribution]
is a continuous distribution with the
is a continuous distribution with the
[@http://en.wikipedia.org/wiki/Probability_density_function probability density function (pdf)]:
f(x; [alpha], [beta]) = [alpha][beta][super [alpha]] / x[super [alpha]+ 1]
For shape parameter [alpha][space] > 0, and location parameter [beta][space] > 0, and [alpha][space] > 0.
For shape parameter [alpha][space] > 0, and scale parameter [beta][space] > 0.
If x < [beta][space], the pdf is zero.
The [@http://mathworld.wolfram.com/paretoDistribution.html Pareto distribution]
The [@http://mathworld.wolfram.com/ParetoDistribution.html Pareto distribution]
often describes the larger compared to the smaller.
A classic example is that 80% of the wealth is owned by 20% of the population.
The following graph illustrates how the PDF varies with the location parameter [beta]:
The following graph illustrates how the PDF varies with the scale parameter [beta]:
[graph pareto_pdf1]
@@ -48,23 +49,23 @@ And this graph illustrates how the PDF varies with the shape parameter [alpha]:
[h4 Related distributions]
[h4 Member Functions]
pareto_distribution(RealType location = 1, RealType shape = 1);
Constructs a [@http://en.wikipedia.org/wiki/pareto_distribution
pareto_distribution(RealType scale = 1, RealType shape = 1);
Constructs a [@http://en.wikipedia.org/wiki/pareto_distribution
pareto distribution] with shape /shape/ and scale /scale/.
Requires that the /shape/ and /scale/ parameters are both greater than zero,
Requires that the /shape/ and /scale/ parameters are both greater than zero,
otherwise calls __domain_error.
RealType location()const;
Returns the /location/ parameter of this distribution.
RealType scale()const;
Returns the /scale/ parameter of this distribution.
RealType shape()const;
Returns the /shape/ parameter of this distribution.
[h4 Non-member Accessors]
@@ -72,19 +73,20 @@ Returns the /shape/ parameter of this distribution.
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The supported domain of the random variable is \[location, [infin]\].
The supported domain of the random variable is \[scale, [infin]\].
[h4 Accuracy]
The pareto distribution is implemented in terms of the
The Pareto distribution is implemented in terms of the
standard library `exp` functions plus __expm1
and as such should have very low error rates
except when probability is very close to unity.
and so should have very small errors, usually only a few epsilon.
If probability is near to unity (or the complement of a probability near zero) see also __why_complements.
[h4 Implementation]
In the following table [alpha][space] is the shape parameter of the distribution, and
[beta][space] is its location parameter, /x/ is the random variate, /p/ is the probability
[beta][space] is its scale parameter, /x/ is the random variate, /p/ is the probability
and its complement /q = 1-p/.
[table
@@ -92,24 +94,26 @@ and its complement /q = 1-p/.
[[pdf][Using the relation: pdf p = [alpha][beta][super [alpha]]/x[super [alpha] +1] ]]
[[cdf][Using the relation: cdf p = 1 - ([beta][space] / x)[super [alpha]] ]]
[[cdf complement][Using the relation: q = 1 - p = -([beta][space] / x)[super [alpha]] ]]
[[quantile][Using the relation: x = [alpha] / (1 - p)[super 1/[beta]] ]]
[[quantile from the complement][Using the relation: x = [alpha] / (q)[super 1/[beta]] ]]
[[quantile][Using the relation: x = [beta] / (1 - p)[super 1/[alpha]] ]]
[[quantile from the complement][Using the relation: x = [beta] / (q)[super 1/[alpha]] ]]
[[mean][[alpha][beta] / ([beta] - 1) ]]
[[variance][[beta][alpha][super 2] / ([beta] - 1)[super 2] ([beta] - 2) ]]
[[mode][[alpha]]]
[[skewness][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
[[kurtosis][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
[[kurtosis excess][Refer to [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
[[skewness][Refer to [@http://mathworld.wolfram.com/ParetoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
[[kurtosis][Refer to [@http://mathworld.wolfram.com/ParetoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
[[kurtosis excess][Refer to [@http://mathworld.wolfram.com/ParetoDistribution.html Weisstein, Eric W. "pareto Distribution." From MathWorld--A Wolfram Web Resource.] ]]
]
[h4 References]
* [@http://en.wikipedia.org/wiki/pareto_distribution Pareto Distribution]
* [@http://mathworld.wolfram.com/paretoDistribution.html Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.]
* Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267.
(Note the meaning of a and b is reversed in Wolfram and Krishnamoorthy).
[endsect][/section:pareto pareto]
[/
Copyright 2006 John Maddock and Paul A. Bristow.
[/
Copyright 2006, 2009 John Maddock and Paul A. Bristow.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt).

15
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@@ -509,14 +509,13 @@ Confidence Estimated Estimated
Value (%) Sample Size Sample Size
(one sided test) (two sided test)
_______________________________________________________________
50.000 2 3
75.000 4 5
90.000 8 10
95.000 12 14
99.000 21 23
99.900 36 38
99.990 51 54
99.999 67 69
75.000 3 4
90.000 7 9
95.000 11 13
99.000 20 22
99.900 35 37
99.990 50 53
99.999 66 68
''']
So in this case, many more measurements would have had to be made,

20
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@@ -257,11 +257,6 @@ would be complex).
[optional_policy]
[caution In addition, the region where ['n > 1] and [phi][space] ['is not in the range]
\[0, [pi]\/2\] is currently unsupported and returns the result of __domain_error.
For this reason it is recomended that you keep [phi][space] inside its "natural" range
of \[0, [pi]\/2\].]
template <class T1, class T2>
``__sf_result`` ellint_3(T1 k, T2 n);
@@ -275,7 +270,7 @@ Returns the complete elliptic integral of the first kind ['[Pi](n, k)]:
Requires ['-1 <= k <= 1] and ['n < 1], otherwise returns the
result of __domain_error (outside this range the result would be complex).
[opitonal_policy]
[optional_policy]
[heading Accuracy]
@@ -322,7 +317,13 @@ Then the relations:
['[Pi](n, -[phi], k) = -[Pi](n, [phi], k)]
['[Pi](n, [phi]+m[pi], k) = [Pi](n, [phi], k) + 2m[Pi](n, k)]
['[Pi](n, [phi]+m[pi], k) = [Pi](n, [phi], k) + 2m[Pi](n, k) ; n <= 1]
['[Pi](n, [phi]+m[pi], k) = [Pi](n, [phi], k) ; n > 1]
[footnote I haven't been able to find a literature reference for this
relation, but it appears to be the convention used by Mathematica.
Intuitively the first ['2 * m * [Pi](n, k)] terms cancel out as the
derivative alternates between +[infin] and -[infin].]
are used to move [phi][space] to the range \[0, [pi]\/2\].
@@ -335,9 +336,4 @@ and
[equation ellint26]
The remaining problem area occurs when n > 1 and [phi][space] is outside
the range \[0, [pi]\/2\]. In this range the reduction formula for
large [phi][space] can no longer be applied. Likewise the identities 17.7.7/8
in A&S for reducing n to the range \[0,1\] appear to be no longer applicable.
[endsect]

5
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@@ -7,8 +7,8 @@
#
# Paths to tools come first, change these to match your system:
#
math2svg='C:\download\open\SVGMath-0.3.1\math2svg.py'
python=/cygdrive/c/Python25/python.exe
math2svg='d:\download\open\SVGMath-0.3.1\math2svg.py'
python=/cygdrive/c/Python26/python.exe
inkscape=/cygdrive/c/progra~1/Inkscape/inkscape
# Image DPI:
dpi=120
@@ -29,3 +29,4 @@ done

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<mi>r</mi>
</mrow>
</mfenced>
</mrow>
<mrow>
<mi>n</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>n</mi>
</mrow>
</mfenced>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>r</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>+</mo>
<mn>6</mn>
</mrow>
</mfenced>
</mrow>
<mrow>
<msup>
<mi>N</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&#x2212;</mo>
<mn>6</mn>
</mrow>
</mfenced>
</mtd>
</mtr>
</mtable>
</mrow>
</math>
</body>
</html>

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@@ -0,0 +1,52 @@
<?xml version='1.0'?>
<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
[<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
<html xmlns='http://www.w3.org/1999/xhtml'>
<head><title>laplace_pdf</title>
</head>
<body>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mtext>f</mtext>
<mfenced>
<mrow>
<mi>x</mi>
<mo>;</mo>
<mi>&#x03BC;</mi>
<mo>,</mo>
<mi>&#x03C3;</mi>
</mrow>
</mfenced>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mfrac>
<mn>1</mn>
<mrow>
<mn>2</mn>
<mi>&#x03C3;</mi>
</mrow>
</mfrac>
<msup>
<mi>e</mi>
<mrow>
<mo>&#x2212;</mo>
<mfrac>
<mrow>
<mo>|</mo>
<mi>x</mi>
<mo>&#x2212;</mo>
<mi>&#x03BC;</mi>
<mo>|</mo>
</mrow>
<mrow>
<mi>&#x03C3;</mi>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</math>
</body>
</html>

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163
doc/sf_and_dist/graphs/dist_graphs.cpp
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@@ -1,5 +1,16 @@
// (C) Copyright John Maddock 2008.
// Copyright Paul A. Bristow 2008
/*! \file dist_graphs.cpp
\brief Produces Scalable Vector Graphic (.svg) files for all distributions.
\details These files can be viewed using most browsers,
though MS Internet Explorer requires a plugin from Adobe.
These file can be converted to .png using Inkscape
(see www.inkscape.org) Export Bit option which by default produces
a Portable Network Graphic file with that same filename but .png suffix instead of .svg.
Using Python, generate.sh does this conversion automatically for all .svg files in a folder.
\author John Maddock and Paul A. Bristow
*/
// Copyright John Maddock 2008.
// Copyright Paul A. Bristow 2008, 2009
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -23,27 +34,30 @@
#include <string>
template <class Dist>
struct is_discrete_distribution
struct is_discrete_distribution
: public boost::mpl::false_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::bernoulli_distribution<T,P> >
struct is_discrete_distribution<boost::math::bernoulli_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::binomial_distribution<T,P> >
struct is_discrete_distribution<boost::math::binomial_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::negative_binomial_distribution<T,P> >
struct is_discrete_distribution<boost::math::negative_binomial_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::poisson_distribution<T,P> >
struct is_discrete_distribution<boost::math::poisson_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::hypergeometric_distribution<T,P> >
: public boost::mpl::true_{};
template <class Dist>
struct value_finder
{
value_finder(Dist const& d, typename Dist::value_type v)
value_finder(Dist const& d, typename Dist::value_type v)
: m_dist(d), m_value(v) {}
inline typename Dist::value_type operator()(const typename Dist::value_type& x)
@@ -79,9 +93,9 @@ public:
//
double mod;
try
{
mod = mode(d);
}
{
mod = mode(d);
}
catch(const std::domain_error& )
{
mod = a;
@@ -96,7 +110,7 @@ public:
double peek_y = pdf(d, mod);
double min_y = peek_y / 20;
//
// If the extent is "infinite" then find out how large it
// If the extent is "infinite" then find out how large it
// has to be for the PDF to decay to min_y:
//
if(a <= -(std::numeric_limits<double>::max)())
@@ -130,7 +144,7 @@ public:
}
//
// Recalculate peek_y and location of mod so that
// it's not too close to one end of the graph:
// it's not too close to one end of the graph:
// otherwise we may be shooting off to infinity.
//
if(!is_discrete_distribution<Dist>::value)
@@ -157,7 +171,7 @@ public:
}
else
{
if(a < m_min_x)
if(a < m_min_x)
m_min_x = a;
if(b > m_max_x)
m_max_x = b;
@@ -168,7 +182,7 @@ public:
{
using namespace boost::svg;
static const svg_color colors[5] =
static const svg_color colors[5] =
{
darkblue,
darkred,
@@ -291,7 +305,7 @@ public:
.line_color(colors[color_index])
.line_width(1.)
.shape(none)
.area_fill(colors[color_index]);
.area_fill(colors[color_index]);
++color_index;
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
}
@@ -307,21 +321,21 @@ private:
int main()
{
distribution_plotter<boost::math::gamma_distribution<> >
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter;
gamma_plotter.add(boost::math::gamma_distribution<>(1), "shape = 0.5");
gamma_plotter.add(boost::math::gamma_distribution<>(2), "shape = 1");
gamma_plotter.add(boost::math::gamma_distribution<>(4), "shape = 3");
gamma_plotter.plot("Gamma Distribution PDF With Scale = 1", "gamma1_pdf.svg");
distribution_plotter<boost::math::gamma_distribution<> >
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter2;
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 0.5), "scale = 2");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 1), "scale = 0.5");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 2), "scale = 2");
gamma_plotter2.plot("Gamma Distribution PDF With Shape = 2", "gamma2_pdf.svg");
distribution_plotter<boost::math::normal>
distribution_plotter<boost::math::normal>
normal_plotter;
normal_plotter.add(boost::math::normal(0, 1), "&#x3BC; = 0, &#x3C3; = 1");
normal_plotter.add(boost::math::normal(0, 0.5), "&#x3BC; = 0, &#x3C3; = 0.5");
@@ -330,7 +344,16 @@ int main()
normal_plotter.add(boost::math::normal(1, 1), "&#x3BC; = 1, &#x3C3; = 1");
normal_plotter.plot("Normal Distribution PDF", "normal_pdf.svg");
distribution_plotter<boost::math::non_central_chi_squared>
distribution_plotter<boost::math::laplace>
laplace_plotter;
laplace_plotter.add(boost::math::laplace(0, 1), "&#x3BC; = 0, &#x3C3; = 1");
laplace_plotter.add(boost::math::laplace(0, 0.5), "&#x3BC; = 0, &#x3C3; = 0.5");
laplace_plotter.add(boost::math::laplace(0, 2), "&#x3BC; = 0, &#x3C3; = 2");
laplace_plotter.add(boost::math::laplace(-1, 1), "&#x3BC; = -1, &#x3C3; = 1");
laplace_plotter.add(boost::math::laplace(1, 1), "&#x3BC; = 1, &#x3C3; = 1");
laplace_plotter.plot("Laplace Distribution PDF", "laplace_pdf.svg");
distribution_plotter<boost::math::non_central_chi_squared>
nc_cs_plotter;
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, &#x3BB;=0");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, &#x3BB;=1");
@@ -340,7 +363,7 @@ int main()
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, &#x3BB;=100");
nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg");
distribution_plotter<boost::math::non_central_beta>
distribution_plotter<boost::math::non_central_beta>
nc_beta_plotter;
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 0), "&#x3B1;=10, &#x3B2;=15, &#x3B4;=0");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 1), "&#x3B1;=10, &#x3B2;=15, &#x3B4;=1");
@@ -350,7 +373,7 @@ int main()
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 100), "&#x3B1;=10, &#x3B2;=15, &#x3B4;=100");
nc_beta_plotter.plot("Non Central Beta PDF", "nc_beta_pdf.svg");
distribution_plotter<boost::math::non_central_f>
distribution_plotter<boost::math::non_central_f>
nc_f_plotter;
nc_f_plotter.add(boost::math::non_central_f(10, 20, 0), "v1=10, v2=20, &#x3BB;=0");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 1), "v1=10, v2=20, &#x3BB;=1");
@@ -360,7 +383,7 @@ int main()
nc_f_plotter.add(boost::math::non_central_f(10, 20, 100), "v1=10, v2=20, &#x3BB;=100");
nc_f_plotter.plot("Non Central F PDF", "nc_f_pdf.svg");
distribution_plotter<boost::math::non_central_t>
distribution_plotter<boost::math::non_central_t>
nc_t_plotter;
nc_t_plotter.add(boost::math::non_central_t(10, -10), "v=10, &#x3B4;=-10");
nc_t_plotter.add(boost::math::non_central_t(10, -5), "v=10, &#x3B4;=-5");
@@ -369,7 +392,7 @@ int main()
nc_t_plotter.add(boost::math::non_central_t(10, 10), "v=10, &#x3B4;=10");
nc_t_plotter.plot("Non Central T PDF", "nc_t_pdf.svg");
distribution_plotter<boost::math::beta_distribution<> >
distribution_plotter<boost::math::beta_distribution<> >
beta_plotter;
beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5");
beta_plotter.add(boost::math::beta_distribution<>(5, 1), "alpha=5, beta=1");
@@ -378,21 +401,21 @@ int main()
beta_plotter.add(boost::math::beta_distribution<>(2, 5), "alpha=2, beta=5");
beta_plotter.plot("Beta Distribution PDF", "beta_pdf.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter;
cauchy_plotter.add(boost::math::cauchy_distribution<>(-5, 1), "location = -5");
cauchy_plotter.add(boost::math::cauchy_distribution<>(0, 1), "location = 0");
cauchy_plotter.add(boost::math::cauchy_distribution<>(5, 1), "location = 5");
cauchy_plotter.plot("Cauchy Distribution PDF (scale = 1)", "cauchy_pdf1.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter2;
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 0.5), "scale = 0.5");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 1), "scale = 1");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 2), "scale = 2");
cauchy_plotter2.plot("Cauchy Distribution PDF (location = 0)", "cauchy_pdf2.svg");
distribution_plotter<boost::math::chi_squared_distribution<> >
distribution_plotter<boost::math::chi_squared_distribution<> >
chi_squared_plotter;
//chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2");
@@ -400,28 +423,28 @@ int main()
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(10), "v=10");
chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg");
distribution_plotter<boost::math::exponential_distribution<> >
distribution_plotter<boost::math::exponential_distribution<> >
exponential_plotter;
exponential_plotter.add(boost::math::exponential_distribution<>(0.5), "&#x3BB;=1");
exponential_plotter.add(boost::math::exponential_distribution<>(1), "&#x3BB;=2");
exponential_plotter.add(boost::math::exponential_distribution<>(2), "&#x3BB;=5");
exponential_plotter.plot("Exponential Distribution PDF", "exponential_pdf.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter;
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(-5), "location=1");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(0), "location=2");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(5), "location=5");
extreme_value_plotter.plot("Extreme Value Distribution PDF (shape=1)", "extreme_value_pdf1.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter2;
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 0.5), "shape=0.5");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 1), "shape=1");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 2), "shape=2");
extreme_value_plotter2.plot("Extreme Value Distribution PDF (location=0)", "extreme_value_pdf2.svg");
distribution_plotter<boost::math::fisher_f_distribution<> >
distribution_plotter<boost::math::fisher_f_distribution<> >
fisher_f_plotter;
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 4), "n=4, m=4");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 4), "n=10, m=4");
@@ -429,35 +452,35 @@ int main()
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 10), "n=4, m=10");
fisher_f_plotter.plot("F Distribution PDF", "fisher_f_pdf.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter;
lognormal_plotter.add(boost::math::lognormal_distribution<>(-1), "location=-1");
lognormal_plotter.add(boost::math::lognormal_distribution<>(0), "location=0");
lognormal_plotter.add(boost::math::lognormal_distribution<>(1), "location=1");
lognormal_plotter.plot("Lognormal Distribution PDF (scale=1)", "lognormal_pdf1.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter2;
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 0.5), "scale=0.5");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 1), "scale=1");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 2), "scale=2");
lognormal_plotter2.plot("Lognormal Distribution PDF (location=0)", "lognormal_pdf2.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter;
pareto_plotter.add(boost::math::pareto_distribution<>(1), "location=1");
pareto_plotter.add(boost::math::pareto_distribution<>(2), "location=2");
pareto_plotter.add(boost::math::pareto_distribution<>(3), "location=3");
pareto_plotter.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf1.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter; // Rely on 2nd parameter shape = 1 default.
pareto_plotter.add(boost::math::pareto_distribution<>(1), "scale=1");
pareto_plotter.add(boost::math::pareto_distribution<>(2), "scale=2");
pareto_plotter.add(boost::math::pareto_distribution<>(3), "scale=3");
pareto_plotter.plot("Pareto Distribution PDF (shape=1)", "pareto_pdf1.svg");
distribution_plotter<boost::math::pareto_distribution<> >
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter2;
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "scale=0.5");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "scale=1");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "scale=2");
pareto_plotter2.plot("Pareto Distribution PDF (location=1)", "pareto_pdf2.svg");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "shape=0.5");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "shape=1");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "shape=2");
pareto_plotter2.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf2.svg");
distribution_plotter<boost::math::rayleigh_distribution<> >
distribution_plotter<boost::math::rayleigh_distribution<> >
rayleigh_plotter;
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(0.5), "&#x3C3;=0.5");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(1), "&#x3C3;=1");
@@ -466,7 +489,7 @@ int main()
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "&#x3C3;=10");
rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg");
distribution_plotter<boost::math::rayleigh_distribution<> >
distribution_plotter<boost::math::rayleigh_distribution<> >
rayleigh_cdf_plotter(false);
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(0.5), "&#x3C3;=0.5");
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(1), "&#x3C3;=1");
@@ -475,7 +498,7 @@ int main()
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "&#x3C3;=10");
rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg");
distribution_plotter<boost::math::triangular_distribution<> >
distribution_plotter<boost::math::triangular_distribution<> >
triangular_plotter;
triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
@@ -484,7 +507,7 @@ int main()
triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg");
distribution_plotter<boost::math::triangular_distribution<> >
distribution_plotter<boost::math::triangular_distribution<> >
triangular_cdf_plotter(false);
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
@@ -493,14 +516,14 @@ int main()
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
triangular_cdf_plotter.plot("Triangular Distribution CDF", "triangular_cdf.svg");
distribution_plotter<boost::math::students_t_distribution<> >
distribution_plotter<boost::math::students_t_distribution<> >
students_t_plotter;
students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1");
students_t_plotter.add(boost::math::students_t_distribution<>(5), "v=5");
students_t_plotter.add(boost::math::students_t_distribution<>(30), "v=30");
students_t_plotter.plot("Students T Distribution PDF", "students_t_pdf.svg");
distribution_plotter<boost::math::weibull_distribution<> >
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter;
weibull_plotter.add(boost::math::weibull_distribution<>(0.75), "shape=0.75");
weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1");
@@ -508,14 +531,14 @@ int main()
weibull_plotter.add(boost::math::weibull_distribution<>(10), "shape=10");
weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg");
distribution_plotter<boost::math::weibull_distribution<> >
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter2;
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2");
weibull_plotter2.plot("Weibull Distribution PDF (shape=3)", "weibull_pdf2.svg");
distribution_plotter<boost::math::uniform_distribution<> >
distribution_plotter<boost::math::uniform_distribution<> >
uniform_plotter;
uniform_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
uniform_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
@@ -523,7 +546,7 @@ int main()
uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg");
distribution_plotter<boost::math::uniform_distribution<> >
distribution_plotter<boost::math::uniform_distribution<> >
uniform_cdf_plotter(false);
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
@@ -531,53 +554,71 @@ int main()
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
uniform_cdf_plotter.plot("Uniform Distribution CDF", "uniform_cdf.svg");
distribution_plotter<boost::math::bernoulli_distribution<> >
distribution_plotter<boost::math::bernoulli_distribution<> >
bernoulli_plotter;
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
bernoulli_plotter.plot("Bernoulli Distribution PDF", "bernoulli_pdf.svg");
distribution_plotter<boost::math::bernoulli_distribution<> >
distribution_plotter<boost::math::bernoulli_distribution<> >
bernoulli_cdf_plotter(false);
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
bernoulli_cdf_plotter.plot("Bernoulli Distribution CDF", "bernoulli_cdf.svg");
distribution_plotter<boost::math::binomial_distribution<> >
distribution_plotter<boost::math::binomial_distribution<> >
binomial_plotter;
binomial_plotter.add(boost::math::binomial_distribution<>(5, 0.5), "n=5 p=0.5");
binomial_plotter.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
binomial_plotter.add(boost::math::binomial_distribution<>(50, 0.5), "n=50 p=0.5");
binomial_plotter.plot("Binomial Distribution PDF", "binomial_pdf_1.svg");
distribution_plotter<boost::math::binomial_distribution<> >
distribution_plotter<boost::math::binomial_distribution<> >
binomial_plotter2;
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.1), "n=20 p=0.1");
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.9), "n=20 p=0.9");
binomial_plotter2.plot("Binomial Distribution PDF", "binomial_pdf_2.svg");
distribution_plotter<boost::math::negative_binomial_distribution<> >
distribution_plotter<boost::math::negative_binomial_distribution<> >
negative_binomial_plotter;
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.25), "n=20 p=0.25");
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5");
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.75), "n=20 p=0.75");
negative_binomial_plotter.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_1.svg");
distribution_plotter<boost::math::negative_binomial_distribution<> >
distribution_plotter<boost::math::negative_binomial_distribution<> >
negative_binomial_plotter2;
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(10, 0.5), "n=10 p=0.5");
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=40 p=0.5");
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(70, 0.5), "n=70 p=0.5");
negative_binomial_plotter2.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_2.svg");
distribution_plotter<boost::math::poisson_distribution<> >
distribution_plotter<boost::math::poisson_distribution<> >
poisson_plotter;
poisson_plotter.add(boost::math::poisson_distribution<>(5), "&#x3BB;=1");
poisson_plotter.add(boost::math::poisson_distribution<>(10), "&#x3BB;=10");
poisson_plotter.add(boost::math::poisson_distribution<>(20), "&#x3BB;=50");
poisson_plotter.plot("Poisson Distribution PDF", "poisson_pdf_1.svg");
distribution_plotter<boost::math::hypergeometric_distribution<> >
hypergeometric_plotter;
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 50, 500), "N=500, r=50, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 100, 500), "N=500, r=100, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 250, 500), "N=500, r=250, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 400, 500), "N=500, r=400, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 450, 500), "N=500, r=450, n=30");
hypergeometric_plotter.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_1.svg");
distribution_plotter<boost::math::hypergeometric_distribution<> >
hypergeometric_plotter2;
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(50, 50, 500), "N=500, r=50, n=50");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(100, 50, 500), "N=500, r=50, n=100");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(250, 50, 500), "N=500, r=50, n=250");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(400, 50, 500), "N=500, r=50, n=400");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450");
hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg");
}

5
doc/sf_and_dist/graphs/generate.sh
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@@ -7,8 +7,8 @@
#
# Paths to tools come first, change these to match your system:
#
math2svg='C:\download\open\SVGMath-0.3.1\math2svg.py'
python=/cygdrive/c/Python25/python.exe
math2svg='d:\download\open\SVGMath-0.3.1\math2svg.py'
python=/cygdrive/c/Python26/python.exe
inkscape=/cygdrive/c/progra~1/Inkscape/inkscape
# Image DPI:
dpi=96
@@ -24,3 +24,4 @@ done

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doc/sf_and_dist/graphs/hypergeometric_pdf_1.svg Normal file
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xmlns:cc="http://web.resource.org/cc/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns ="http://www.w3.org/2000/svg"
>
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<!-- Boost Software License, Version 1.0.-->
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<text x="59.2" y="163.8" text-anchor="end" font-size="12" font-family="Verdana">0.7</text>
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<text x="59.2" y="89.25" text-anchor="end" font-size="12" font-family="Verdana">1</text>
<text x="59.2" y="64.4" text-anchor="end" font-size="12" font-family="Verdana">1.1</text>
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<text x="310.2" y="388" text-anchor="middle" font-size="14" font-family="Verdana">Random Variable</text></g>
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L445.0,233.4 L445.7,235.6 L446.3,237.7 L446.9,239.8 L447.6,241.8 L448.2,243.8 L448.9,245.8 L449.5,247.7
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L460.4,275.0 L461.0,276.3 L461.6,277.6 L462.3,278.9 L462.9,280.2 L463.6,281.4 L464.2,282.6 L464.8,283.8
L465.5,284.9 L466.1,286.1 L466.8,287.2 L467.4,288.3 L468.0,289.4 L468.7,290.4 L469.3,291.4 L469.9,292.5
L470.6,293.4 L471.2,294.4 L471.9,295.4 L472.5,296.3 L473.1,297.2 L473.8,298.1 L474.4,299.0 L475.1,299.8
L475.7,300.7 L476.3,301.5 L477.0,302.3 L477.6,303.1 L478.3,303.9 L478.9,304.7 L479.5,305.4 L480.2,306.1
L480.8,306.8 L481.5,307.6 L482.1,308.2 L482.7,308.9 L483.4,309.6 L484.0,310.2 L484.7,310.9 L485.3,311.5
L485.9,312.1 L486.6,312.7 L487.2,313.3 L487.8,313.9 L488.5,314.4 L489.1,315.0 L489.8,315.5 L490.4,316.1
L491.0,316.6 L491.7,317.1 L492.3,317.6 L493.0,318.1 L493.6,318.6 L494.2,319.0 L494.9,319.5 L495.5,320.0
L496.2,320.4 L496.8,320.8 L497.4,321.3 L498.1,321.7 L498.7,322.1 L499.4,322.5 L500.0,322.9 L500.6,323.3
L501.3,323.7 L501.9,324.0 L502.6,324.4 L503.2,324.7 L503.8,325.1 L504.5,325.4 L505.1,325.8 L505.7,326.1
L506.4,326.4 L507.0,326.7 L507.7,327.1 L508.3,327.4 L508.9,327.7 L509.6,327.9 L510.2,328.2 L510.9,328.5
L511.5,328.8 L512.1,329.1 L512.8,329.3 L513.4,329.6 L514.1,329.8 L514.7,330.1 L515.3,330.3 L516.0,330.6
L516.6,330.8 L517.3,331.0 L517.9,331.3 L518.5,331.5 L519.2,331.7 L519.8,331.9 L520.5,332.1 L521.1,332.3
L521.7,332.5 L522.4,332.7 L523.0,332.9 L523.6,333.1 L524.3,333.3 L524.9,333.5 L525.6,333.6 L526.2,333.8
L526.8,334.0 L527.5,334.1 L528.1,334.3 L528.8,334.5 L529.4,334.6 L530.0,334.8 L530.7,334.9 L531.3,335.1
L532.0,335.2 L532.6,335.4 L533.2,335.5 L533.9,335.6 L534.5,335.8 L535.2,335.9 L535.8,336.0 L536.4,336.2
L537.1,336.3 L537.7,336.4 L538.4,336.5 L539.0,336.6 L539.6,336.8 L540.3,336.9 L540.9,337.0 L541.5,337.1
L542.2,337.2 L542.8,337.3 L543.5,337.4 L544.1,337.5 L544.7,337.6 L545.4,337.7 L546.0,337.8 L546.7,337.9
L547.3,338.0 L547.9,338.0 L548.6,338.1 L549.2,338.2 L549.9,338.3 L550.5,338.4 L551.1,338.5 L551.8,338.5
L552.4,338.6 L553.1,338.7 L553.7,338.8 L554.3,338.8 L555.0,338.9 L555.6,339.0 L556.3,339.0 L556.9,339.1
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L711.0,342.4 L711.6,342.4 L712.2,342.4 L712.9,342.4 L713.5,342.4 L714.2,342.4 L714.8,342.4 L715.4,342.4
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L726.3,342.4 L726.9,342.4 L727.6,342.4 L728.2,342.4 L728.9,342.4 L729.5,342.4 L730.1,342.4 L730.8,342.4
L731.4,342.4 L732.1,342.4 L732.7,342.4 '></path>
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<text><tspan>&#956; = 2, &#963; = 4</tspan>
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<path d='M93.4,16.6 L93.4,342.4 L732.7,342.4 L732.7,16.6 L93.4,16.6 Z '></path>
<g transform="translate(39.1,179.5) rotate(-90)" style="stroke:none; fill:black; font-family:Arial; font-size:12.00pt; text-anchor:middle">
<text><tspan>Probability</tspan>
</text>
</g>
<g transform="translate(413.0,391.9)" style="stroke:none; fill:black; font-family:Arial; font-size:12.00pt; text-anchor:middle">
<text><tspan>Random Variable</tspan>
</text>
</g>
</g>
<g style="fill:none; color:red; stroke:currentColor; stroke-width:1.00; stroke-linecap:butt; stroke-linejoin:miter">
</g>
<g style="fill:none; color:black; stroke:currentColor; stroke-width:1.00; stroke-linecap:butt; stroke-linejoin:miter">
<g transform="translate(665.6,39.1)" style="stroke:none; fill:black; font-family:Arial; font-size:12.00pt; text-anchor:end">
<text><tspan>&#956; = 0, &#963; = 1</tspan>
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</g>
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<text x="337.7" y="388" text-anchor="middle" font-size="14" font-family="Verdana">Random Variable</text></g>
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@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Math Toolkit</title>
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</head>
@@ -42,11 +42,18 @@
<div class="author"><h3 class="author">
<span class="firstname">Johan</span> <span class="surname">Råde</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Gautam</span> <span class="surname">Sewani</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Thijs</span> <span class="surname">van den Berg</span>
</h3></div>
</div></div>
<div><p class="copyright">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde</p></div>
<div><p class="copyright">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg</p></div>
<div><div class="legalnotice">
<a name="id527114"></a><p>
<a name="id761748"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
@@ -72,9 +79,12 @@
and Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/threads.html"> Thread Safety</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/perf_over.html"> Performance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/building.html"> If and How to Build
the Library and its Examples and Tests</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/history1.html"> History and What's
New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/tr1.html"> C99 and TR1 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/tr1.html"> C99 and C++ TR1 C-style
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_overview/contact.html"> Contact Info and
Support</a></span></dt>
</dl></dd>
@@ -83,7 +93,20 @@
<dt><span class="section"><a href="math_toolkit/dist/stat_tut.html"> Statistical Distributions
Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview.html"> Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview.html"> Overview of Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/headers.html"> Headers
and Namespaces</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/objects.html"> Distributions
are Objects</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/generic.html"> Generic
operations common to all distributions are non-member functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/complements.html">
Complements are supported too - and when to use them</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/parameters.html">
Parameters can be calculated</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/overview/summary.html"> Summary</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg.html"> Worked Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/dist_construct_eg.html">
@@ -108,6 +131,8 @@
and Scale Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/nag_library.html"> Comparison
with C, R, FORTRAN-style Free Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/weg/c_sharp.html"> Using the
Distributions from Within C#</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist/stat_tut/variates.html"> Random Variates
and Distribution Parameters</a></span></dt>
@@ -137,6 +162,12 @@
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/f_dist.html"> F Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/gamma_dist.html"> Gamma
(and Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html">
Hypergeometric Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/laplace_dist.html"> Laplace
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/logistic_dist.html">
Logistic Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/lognormal_dist.html">
Log Normal Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html">
@@ -287,39 +318,43 @@
<dt><span class="section"><a href="math_toolkit/special/inv_hyper/asinh.html"> asinh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/inv_hyper/atanh.html"> atanh</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/special/rounding.html"> Rounding Truncation and
</dl></dd>
<dt><span class="section"><a href="math_toolkit/utils.html"> Floating Point Utilities</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/utils/rounding.html"> Rounding Truncation and
Integer Conversion</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/special/rounding/round.html"> Rounding Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/rounding/trunc.html"> Truncation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/rounding/modf.html"> Integer and Fractional
<dt><span class="section"><a href="math_toolkit/utils/rounding/round.html"> Rounding Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/utils/rounding/trunc.html"> Truncation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/utils/rounding/modf.html"> Integer and Fractional
Part Splitting (modf)</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/special/fpclass.html"> Floating-Point Classification:
<dt><span class="section"><a href="math_toolkit/utils/fpclass.html"> Floating-Point Classification:
Infinities and NaN's</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/next_float.html"> Floating-Point Representation
<dt><span class="section"><a href="math_toolkit/utils/sign_functions.html"> Sign Manipulation
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/utils/next_float.html"> Floating-Point Representation
Distance (ULP), and Finding Adjacent Floating-Point Values</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/special/next_float/nextafter.html"> Finding
the Next Representable Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/next_float/float_next.html"> Finding
<dt><span class="section"><a href="math_toolkit/utils/next_float/nextafter.html"> Finding the
Next Representable Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/utils/next_float/float_next.html"> Finding
the Next Greater Representable Value (float_next)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/next_float/float_prior.html"> Finding
<dt><span class="section"><a href="math_toolkit/utils/next_float/float_prior.html"> Finding
the Next Smaller Representable Value (float_prior)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/next_float/float_distance.html"> Calculating
<dt><span class="section"><a href="math_toolkit/utils/next_float/float_distance.html"> Calculating
the Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/next_float/float_advance.html"> Advancing
<dt><span class="section"><a href="math_toolkit/utils/next_float/float_advance.html"> Advancing
a Floating Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/special/extern_c.html"> TR1 and C99 external
"C" Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/special/extern_c/tr1.html"> C99 and TR1 C Functions
Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/extern_c/c99.html"> C99 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/special/extern_c/tr1_ref.html"> TR1 C Functions
Quick Reference</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/extern_c.html"> TR1 and C99 external "C"
Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/extern_c/tr1.html"> C99 and TR1 C Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/extern_c/c99.html"> C99 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/extern_c/tr1_ref.html"> TR1 C Functions Quick
Reference</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/toolkit.html"> Internal Details and Tools (Experimental)</a></span></dt>
<dd><dl>
@@ -357,6 +392,8 @@
<dd><dl>
<dt><span class="section"><a href="math_toolkit/using_udt/use_ntl.html"> Using With NTL - a High-Precision
Floating-Point Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/using_udt/use_mpfr.html"> Using With MPFR / GMP
- a High-Precision Floating-Point Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/using_udt/concepts.html"> Conceptual Requirements
for Real Number Types</a></span></dt>
<dt><span class="section"><a href="math_toolkit/using_udt/dist_concept.html"> Conceptual Requirements
@@ -451,7 +488,7 @@
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: December 29, 2008 at 16:50:38 GMT</small></p></td>
<td align="left"><p><small>Last revised: May 22, 2009 at 11:23:00 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

7
doc/sf_and_dist/html/math_toolkit/backgrounders.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Backgrounders</title>
<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../index.html" title="Math Toolkit">
<link rel="up" href="../index.html" title="Math Toolkit">
<link rel="prev" href="perf/perf_test_app.html" title="The Performance Test Application">
@@ -38,8 +38,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

88
doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Additional Implementation Notes</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="../backgrounders.html" title="Backgrounders">
@@ -33,7 +33,7 @@
and reflect more the general implementation philosophy used.
</p>
<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
<a name="id887352"></a>
<a name="id1140046"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
philosophy</a>
</h5>
@@ -85,7 +85,7 @@
These could still provide sufficient accuracy for some speed-critical applications.
</p>
<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
<a name="id887463"></a>
<a name="id1140110"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
and Representation of Test Values</a>
</h5>
@@ -130,7 +130,7 @@
binary value).
</p>
<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
<a name="id887695"></a>
<a name="id1140254"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
of Tests</a>
</h5>
@@ -156,7 +156,7 @@
first that the suffix L is present, and then that the tolerance is big enough.
</p>
<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
<a name="id887755"></a>
<a name="id1140291"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
Unsuitable Arguments</a>
</h5>
@@ -242,7 +242,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
<a name="id887972"></a>
<a name="id1140424"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
of Functions that are Not Mathematically defined</a>
</h5>
@@ -276,7 +276,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
<a name="id888113"></a>
<a name="id1140509"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
of distributions</a>
</h5>
@@ -309,7 +309,7 @@
Basic Statistics.</a> give more detail, in particular for discrete distributions.
</p>
<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
<a name="id888257"></a>
<a name="id1140606"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
of Floating-Point Infinity</a>
</h5>
@@ -353,7 +353,7 @@
handling policies</a>.
</p>
<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
<a name="id888415"></a>
<a name="id1140693"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
Shape and Location</a>
</h5>
@@ -380,7 +380,7 @@
functions, they can be added if required.
</p>
<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
<a name="id888878"></a>
<a name="id1141231"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
on Implementation of Specific Functions &amp; Distributions</a>
</h5>
@@ -392,7 +392,7 @@
0 and upper = 1 would be more suitable.
</li></ul></div>
<a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a><h5>
<a name="id888919"></a>
<a name="id1141251"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
Approximations Used</a>
</h5>
@@ -435,7 +435,7 @@
to the "true" minimax solution.
</p>
<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
<a name="id889015"></a>
<a name="id1141296"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
of Mathematical Constants</a>
</h5>
@@ -469,7 +469,7 @@
<pre class="programlisting"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">pi</span><span class="special">,</span>
<span class="number">3.141592653589793238462643383279502884197169399375105820974944</span><span class="special">,</span>
<span class="number">5923078164062862089986280348253421170679821480865132823066470938446095505</span><span class="special">,</span>
<span class="number">0</span><span class="special">)</span>
<span class="number">0</span><span class="special">)</span>
</pre>
<p>
And used thus:
@@ -487,16 +487,16 @@
<p>
So you cannot write
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;&gt;();</span> <span class="comment">// could not deduce template argument for 'T'
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">&lt;&gt;();</span> <span class="comment">// could not deduce template argument for 'T'
</span></pre>
<p>
Neither can you write:
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> <span class="comment">// Context does not allow for disambiguation of overloaded function
</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">();</span> <span class="comment">// Context does not allow for disambiguation of overloaded function
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> <span class="comment">// Context does not allow for disambiguation of overloaded function
</span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">();</span> <span class="comment">// Context does not allow for disambiguation of overloaded function
</span></pre>
<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
<a name="id889570"></a>
<a name="id1141682"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
safety</a>
</h5>
@@ -521,7 +521,7 @@
the right thing here at some point.
</p>
<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
<a name="id889635"></a>
<a name="id1141718"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
of Test Data</a>
</h5>
@@ -565,7 +565,7 @@
the underlying special function is known to be difficult to implement.
</p>
<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
<a name="id889746"></a>
<a name="id1141785"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
and Managing the Equations</a>
</h5>
@@ -582,7 +582,7 @@
Convertion to SVG was achieved using <a href="http://www.grigoriev.ru/svgmath/" target="_top">SVGMath</a>
and a command line such as:
</p>
<pre class="programlisting">$for file in *.mml; do
<pre class="programlisting">$for file in *.mml; do
&gt;/cygdrive/c/Python25/python.exe 'C:\download\open\SVGMath-0.3.1\math2svg.py' \
&gt;&gt;$file &gt; $(basename $file .mml).svg
&gt;done
@@ -629,8 +629,8 @@
<p>
Or using Inkscape and a command such as:
</p>
<pre class="programlisting">for file in *.svg; do
/cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
<pre class="programlisting">for file in *.svg; do
/cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file);
done</pre>
<p>
Currently Inkscape seems to generate the better looking png's.
@@ -639,20 +639,29 @@ done</pre>
The PDF is generated into \pdf\math.pdf using a command from a shell or command
window with current directory \math_toolkit\libs\math\doc\sf_and_dist, typically:
</p>
<pre class="programlisting">bjam -a pdf</pre>
<pre class="programlisting">bjam -a pdf &gt;math_pdf.log</pre>
<p>
Note that XEP will have to be configured to <span class="bold"><strong>use and
embed</strong></span> whatever fonts are used by the SVG equations (if necessary
editing the sample xep.xml provided by the XEP installation).
embed</strong></span> whatever fonts are used by the SVG equations (almost certainly
editing the sample xep.xml provided by the XEP installation). If you fail
to do this you will get XEP warnings in the log file like
</p>
<pre class="programlisting">[warning]could not find any font family matching "Times New Roman"; replaced by Helvetica</pre>
<p>
(html is the default so it is generated at math_toolkit\libs\math\doc\sf_and_dist\html\index.html
using command line &gt;bjam -a &gt; math_docs.log).
</p>
<pre class="programlisting"><span class="special">&lt;!--</span> <span class="identifier">Sample</span> <span class="identifier">configuration</span> <span class="keyword">for</span> <span class="identifier">Windows</span> <span class="identifier">TrueType</span> <span class="identifier">fonts</span><span class="special">.</span> <span class="special">--&gt;</span>
</pre>
<p>
&lt;!-- Sample configuration for Windows TrueType fonts. --&gt; is provided
in the xep.xml downloaded, but the Windows TrueType fonts are commented out.
</p>
<p>
(html is generated at math_toolkit\libs\math\doc\sf_and_dist\html\index.html
using just bjam -a).
JM's XEP config file \xep\xep.xml has the following font configuration section
added:
</p>
<p>
JM's XEP config file has the following font configuration section added:
</p>
<pre class="programlisting">&lt;font-group xml:base="file:/C:/Windows/Fonts/" label="Windows TrueType" embed="true" subset="true"&gt;
<pre class="programlisting">&lt;font-group xml:base="file:/C:/Windows/Fonts/" label="Windows TrueType" embed="true" subset="true"&gt;
&lt;font-family name="Arial"&gt;
&lt;font&gt;&lt;font-data ttf="arial.ttf"/&gt;&lt;/font&gt;
&lt;font style="oblique"&gt;&lt;font-data ttf="ariali.ttf"/&gt;&lt;/font&gt;
@@ -692,14 +701,16 @@ done</pre>
&lt;font weight="bold"&gt;&lt;font-data ttf="palab.ttf"/&gt;&lt;/font&gt;
&lt;font weight="bold" style="italic"&gt;&lt;font-data ttf="palabi.ttf"/&gt;&lt;/font&gt;
&lt;/font-family&gt;
&lt;font-family name="Lucida Sans Unicode"&gt;
&lt;font&gt;&lt;font-data ttf="lsansuni.ttf"/&gt;&lt;/font&gt;
&lt;font-family name<code class="literal">"Lucida Sans Unicode"&gt;
&lt;!-- &lt;font&gt;&lt;font-data ttf</code>"lsansuni.ttf"&gt;&lt;<span class="emphasis"><em>font&gt; --&gt;
&lt;!-- actually called l_10646.ttf on Windows 2000 and Vista Sp1 --&gt;
&lt;font&gt;&lt;font-data ttf="l_10646.ttf"</em></span>&gt;&lt;/font&gt;
&lt;/font-family&gt;
</pre>
<p>
PAB had to alter his because the Lucida Sans Unicode font had a different
name. Changes are very likely to be required if you are not using Windows.
name. Other changes are very likely to be required if you are not using Windows.
</p>
<p>
XZ authored his equations using the venerable Latex, JM converted these to
@@ -726,7 +737,7 @@ done</pre>
HTML: this needs further investigation.
</p>
<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
<a name="id890132"></a>
<a name="id1142031"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
Graphs</a>
</h5>
@@ -743,8 +754,9 @@ done</pre>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

21
doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>The Lanczos Approximation</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="relative_error.html" title="Relative Error">
@@ -27,7 +27,7 @@
<a name="math_toolkit.backgrounders.lanczos"></a><a class="link" href="lanczos.html" title="The Lanczos Approximation"> The Lanczos Approximation</a>
</h3></div></div></div>
<a name="math_toolkit.backgrounders.lanczos.motivation"></a><h5>
<a name="id890490"></a>
<a name="id1142254"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
</h5>
<p>
@@ -98,7 +98,7 @@
functions divided by large powers into single (simpler) expressions.
</p>
<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
<a name="id890868"></a>
<a name="id1142504"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
Approximation</a>
</h5>
@@ -160,7 +160,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
<a name="id891130"></a>
<a name="id1142696"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
the Coefficients</a>
</h5>
@@ -204,7 +204,7 @@
multiplied by <span class="emphasis"><em>F</em></span> as the last step.
</p>
<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
<a name="id891336"></a>
<a name="id1142853"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
the Right Parameters</a>
</h5>
@@ -228,7 +228,7 @@
computing to float precision with double precision arithmetic.
</p>
<div class="table">
<a name="id891419"></a><p class="title"><b>Table 53. Optimal choices for N and g when computing with
<a name="id1142907"></a><p class="title"><b>Table 53. Optimal choices for N and g when computing with
guard digits (source: Pugh)</b></p>
<div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with
guard digits (source: Pugh)">
@@ -371,7 +371,7 @@
exactly matches the machine epsilon for the type in question.
</p>
<div class="table">
<a name="id891741"></a><p class="title"><b>Table 54. Optimum value for N and g when computing at fixed
<a name="id1143118"></a><p class="title"><b>Table 54. Optimum value for N and g when computing at fixed
precision</b></p>
<div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed
precision">
@@ -536,7 +536,7 @@
is exact, and so isn't used for the gamma function.
</p>
<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
<a name="id892020"></a>
<a name="id1143688"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
</h5>
<a name="godfrey"></a><a name="pugh"></a><div class="orderedlist"><ol type="1">
@@ -561,8 +561,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

13
doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>References</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="remez.html" title="The Remez Method">
@@ -27,7 +27,7 @@
<a name="math_toolkit.backgrounders.refs"></a><a class="link" href="refs.html" title="References"> References</a>
</h3></div></div></div>
<a name="math_toolkit.backgrounders.refs.general_references"></a><h5>
<a name="id893418"></a>
<a name="id1144558"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
references</a>
</h5>
@@ -91,7 +91,7 @@
Library (version 2), Walter E. Brown</a>
</p>
<a name="math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__"></a><h5>
<a name="id893592"></a>
<a name="id1144654"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__">Calculators*
that we found (and used to cross-check - as far as their widely-varying accuracy
allowed).</a>
@@ -101,7 +101,7 @@
Binomial Probability Distribution Calculator.
</p>
<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
<a name="id893637"></a>
<a name="id1144680"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
</h5>
<p>
@@ -161,8 +161,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

9
doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Relative Error</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="implementation.html" title="Additional Implementation Notes">
@@ -81,7 +81,7 @@
<a name="zero_error"></a><p>
</p>
<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
<a name="id890412"></a>
<a name="id1142211"></a>
<a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
Impossibility of Zero Error</a>
</h5>
@@ -109,8 +109,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

23
doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>The Remez Method</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="lanczos.html" title="The Lanczos Approximation">
@@ -94,7 +94,7 @@
are located!</em></span>
</p>
<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
<a name="id892271"></a>
<a name="id1143848"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
Method</a>
</h5>
@@ -174,7 +174,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
<a name="id892496"></a>
<a name="id1143999"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
1</a>
</h5>
@@ -205,7 +205,7 @@
to 5.6x10<sup>-4</sup>.
</p>
<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
<a name="id892601"></a>
<a name="id1144074"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
2</a>
</h5>
@@ -234,7 +234,7 @@
In our example we perform multi-point exchange.
</p>
<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
<a name="id892662"></a>
<a name="id1144106"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
</h5>
<p>
@@ -250,7 +250,7 @@
<span class="inlinemediaobject"><img src="../../../graphs/remez-4.png" alt="remez-4"></span>
</p>
<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
<a name="id892723"></a>
<a name="id1144150"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
Approximations</a>
</h5>
@@ -299,7 +299,7 @@
number of terms overall.
</p>
<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
<a name="id892846"></a>
<a name="id1144230"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
Considerations</a>
</h5>
@@ -407,7 +407,7 @@
desired minimax solution (5x10<sup>-4</sup>).
</p>
<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
<a name="id893122"></a>
<a name="id1144386"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
Method Checklist</a>
</h5>
@@ -461,7 +461,7 @@
</li>
</ul></div>
<a name="math_toolkit.backgrounders.remez.references"></a><h5>
<a name="id893237"></a>
<a name="id1144438"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
</h5>
<p>
@@ -527,8 +527,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

30
doc/sf_and_dist/html/math_toolkit/dist.html
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Statistical Distributions and Functions</title>
<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../index.html" title="Math Toolkit">
<link rel="up" href="../index.html" title="Math Toolkit">
<link rel="prev" href="main_overview/contact.html" title="Contact Info and Support">
@@ -30,7 +30,20 @@
<dt><span class="section"><a href="dist/stat_tut.html"> Statistical Distributions
Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="dist/stat_tut/overview.html"> Overview</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview.html"> Overview of Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="dist/stat_tut/overview/headers.html"> Headers
and Namespaces</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview/objects.html"> Distributions
are Objects</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview/generic.html"> Generic
operations common to all distributions are non-member functions</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview/complements.html">
Complements are supported too - and when to use them</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview/parameters.html">
Parameters can be calculated</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/overview/summary.html"> Summary</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="dist/stat_tut/weg.html"> Worked Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="dist/stat_tut/weg/dist_construct_eg.html">
@@ -111,6 +124,8 @@
</dl></dd>
<dt><span class="section"><a href="dist/stat_tut/weg/nag_library.html"> Comparison
with C, R, FORTRAN-style Free Functions</a></span></dt>
<dt><span class="section"><a href="dist/stat_tut/weg/c_sharp.html"> Using the
Distributions from Within C#</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="dist/stat_tut/variates.html"> Random Variates
and Distribution Parameters</a></span></dt>
@@ -140,6 +155,12 @@
<dt><span class="section"><a href="dist/dist_ref/dists/f_dist.html"> F Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/gamma_dist.html"> Gamma
(and Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/hypergeometric_dist.html">
Hypergeometric Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/laplace_dist.html"> Laplace
Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/logistic_dist.html">
Logistic Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/lognormal_dist.html">
Log Normal Distribution</a></span></dt>
<dt><span class="section"><a href="dist/dist_ref/dists/negative_binomial_dist.html">
@@ -177,8 +198,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

13
doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Statistical Distributions Reference</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
<link rel="prev" href="stat_tut/dist_params.html" title="Discrete Probability Distributions">
@@ -48,6 +48,12 @@
<dt><span class="section"><a href="dist_ref/dists/f_dist.html"> F Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/gamma_dist.html"> Gamma
(and Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/hypergeometric_dist.html">
Hypergeometric Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/laplace_dist.html"> Laplace
Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/logistic_dist.html">
Logistic Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/lognormal_dist.html">
Log Normal Distribution</a></span></dt>
<dt><span class="section"><a href="dist_ref/dists/negative_binomial_dist.html">
@@ -83,8 +89,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

13
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Distribution Algorithms</title>
<link rel="stylesheet" href="../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="dists/uniform_dist.html" title="Uniform Distribution">
@@ -28,7 +28,7 @@
Algorithms</a>
</h4></div></div></div>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a><h5>
<a name="id676368"></a>
<a name="id925166"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding
the Location and Scale for Normal and similar distributions</a>
</h5>
@@ -50,7 +50,7 @@
</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Will be needed by users who want to use complements.
</span></pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5>
<a name="id676522"></a>
<a name="id925264"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
function</a>
</h5>
@@ -80,7 +80,7 @@
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5>
<a name="id677143"></a>
<a name="id925709"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
function</a>
</h5>
@@ -130,8 +130,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

13
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Distributions</title>
<link rel="stylesheet" href="../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="nmp.html" title="Non-Member Properties">
@@ -44,6 +44,12 @@
<dt><span class="section"><a href="dists/f_dist.html"> F Distribution</a></span></dt>
<dt><span class="section"><a href="dists/gamma_dist.html"> Gamma
(and Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="dists/hypergeometric_dist.html">
Hypergeometric Distribution</a></span></dt>
<dt><span class="section"><a href="dists/laplace_dist.html"> Laplace
Distribution</a></span></dt>
<dt><span class="section"><a href="dists/logistic_dist.html">
Logistic Distribution</a></span></dt>
<dt><span class="section"><a href="dists/lognormal_dist.html">
Log Normal Distribution</a></span></dt>
<dt><span class="section"><a href="dists/negative_binomial_dist.html">
@@ -76,8 +82,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

17
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Bernoulli Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="../dists.html" title="Distributions">
@@ -87,7 +87,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/bernoulli_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a><h5>
<a name="id628878"></a>
<a name="id871080"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
Functions</a>
</h5>
@@ -103,7 +103,7 @@
Returns the <span class="emphasis"><em>success_fraction</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a><h5>
<a name="id628994"></a>
<a name="id871158"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -128,7 +128,7 @@
exception and make an error message available.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a><h5>
<a name="id629170"></a>
<a name="id871261"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -136,7 +136,7 @@
and so should have errors within an epsilon or two.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a><h5>
<a name="id629201"></a>
<a name="id871282"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
</h5>
<p>
@@ -327,7 +327,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a><h5>
<a name="id629572"></a>
<a name="id871593"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -339,8 +339,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

27
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Beta Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="bernoulli_dist.html" title="Bernoulli Distribution">
@@ -133,12 +133,12 @@
from the centre (where x = half).
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a><h5>
<a name="id630720"></a>
<a name="id872401"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor"></a><h6>
<a name="id630746"></a>
<a name="id872416"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
</h6>
<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">);</span>
@@ -165,7 +165,7 @@
yellow in the graph above).
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a><h6>
<a name="id630928"></a>
<a name="id872532"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
Accessors</a>
</h6>
@@ -189,7 +189,7 @@
</span><span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">beta</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span> <span class="comment">// mybeta.beta() returns 5
</span></pre>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a><h5>
<a name="id631204"></a>
<a name="id872733"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
Estimators</a>
</h5>
@@ -242,7 +242,7 @@ from presumed-known mean and variance.
Returns the value of &#946; that gives: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">beta_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">beta</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">probability</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a><h5>
<a name="id631838"></a>
<a name="id874928"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions">Non-member
Accessor Functions</a>
</h5>
@@ -264,7 +264,7 @@ from presumed-known mean and variance.
Mathworld</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a><h5>
<a name="id632016"></a>
<a name="id875030"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
</h5>
<p>
@@ -277,7 +277,7 @@ from presumed-known mean and variance.
statistical inference</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a><h5>
<a name="id632062"></a>
<a name="id875055"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
distributions</a>
</h5>
@@ -303,7 +303,7 @@ from presumed-known mean and variance.
Distribution</a> with its p parameter set to x.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a><h5>
<a name="id632151"></a>
<a name="id875102"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -315,7 +315,7 @@ from presumed-known mean and variance.
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a><h5>
<a name="id632230"></a>
<a name="id875146"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
</h5>
<p>
@@ -597,7 +597,7 @@ from presumed-known mean and variance.
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
<a name="id633527"></a>
<a name="id876154"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
</h5>
<p>
@@ -615,8 +615,9 @@ from presumed-known mean and variance.
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

33
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Binomial Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="beta_dist.html" title="Beta Distribution">
@@ -167,12 +167,12 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a><h5>
<a name="id634857"></a>
<a name="id877941"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct"></a><h6>
<a name="id634883"></a>
<a name="id877959"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
@@ -189,7 +189,7 @@
otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a><h6>
<a name="id635044"></a>
<a name="id878077"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -205,7 +205,7 @@
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
<a name="id635159"></a>
<a name="id878157"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction">Lower
Bound on the Success Fraction</a>
</h6>
@@ -311,7 +311,7 @@
limits illustrated in the case of the binomial. Biometrika 26 404-413.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a><h6>
<a name="id635812"></a>
<a name="id878606"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction">Upper
Bound on the Success Fraction</a>
</h6>
@@ -389,7 +389,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes"></a><h6>
<a name="id636252"></a>
<a name="id878917"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes">Estimating
the Number of Trials Required for a Certain Number of Successes</a>
</h6>
@@ -431,7 +431,7 @@
of seeing 10 events that occur with frequency one half.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes"></a><h6>
<a name="id636526"></a>
<a name="id879116"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes">Estimating
the Maximum Number of Trials to Ensure no more than a Certain Number
of Successes</a>
@@ -479,7 +479,7 @@
Worked Example.</a>
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
<a name="id636818"></a>
<a name="id879324"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -504,7 +504,7 @@
in the context of this distribution:
</p>
<div class="table">
<a name="id637031"></a><p class="title"><b>Table 11. Meaning of the non-member accessors</b></p>
<a name="id879456"></a><p class="title"><b>Table 11. Meaning of the non-member accessors</b></p>
<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors">
<colgroup>
<col>
@@ -627,7 +627,7 @@
</table></div>
</div>
<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
<a name="id637597"></a>
<a name="id879871"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
</h5>
<p>
@@ -635,7 +635,7 @@
examples</a> are available illustrating the use of the binomial distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a><h5>
<a name="id637637"></a>
<a name="id879892"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -645,7 +645,7 @@
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
<a name="id637686"></a>
<a name="id879921"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
</h5>
<p>
@@ -886,7 +886,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
<a name="id639025"></a>
<a name="id882479"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -907,8 +907,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

17
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Cauchy-Lorentz Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="binomial_dist.html" title="Binomial Distribution">
@@ -88,7 +88,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/cauchy_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a><h5>
<a name="id639735"></a>
<a name="id882987"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
Functions</a>
</h5>
@@ -114,7 +114,7 @@
Returns the scale parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a><h5>
<a name="id639946"></a>
<a name="id883134"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -151,7 +151,7 @@
The domain of the random variable is [-[max_value], +[min_value]].
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a><h5>
<a name="id640200"></a>
<a name="id883281"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -160,7 +160,7 @@
have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a><h5>
<a name="id640256"></a>
<a name="id883314"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
</h5>
<p>
@@ -276,7 +276,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a><h5>
<a name="id640545"></a>
<a name="id883539"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -291,8 +291,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

19
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Chi Squared Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution">
@@ -87,7 +87,7 @@ independent, normally distributed random
<span class="inlinemediaobject"><img src="../../../../../graphs/chi_squared_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a><h5>
<a name="id641321"></a>
<a name="id885201"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
Functions</a>
</h5>
@@ -170,7 +170,7 @@ independent, normally distributed random
NIST Engineering Statistics Handbook, Section 7.2.3.2</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a><h5>
<a name="id641762"></a>
<a name="id885527"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -196,7 +196,7 @@ independent, normally distributed random
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a><h5>
<a name="id641951"></a>
<a name="id885630"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
</h5>
<p>
@@ -204,7 +204,7 @@ independent, normally distributed random
are available illustrating the use of the Chi Squared Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a><h5>
<a name="id641992"></a>
<a name="id885656"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -212,7 +212,7 @@ independent, normally distributed random
gamma functions</a>: please refer to the accuracy data for those functions.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a><h5>
<a name="id642034"></a>
<a name="id885680"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
@@ -379,7 +379,7 @@ independent, normally distributed random
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a><h5>
<a name="id642378"></a>
<a name="id885959"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -394,8 +394,9 @@ independent, normally distributed random
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

17
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Exponential Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
@@ -71,7 +71,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/exponential_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a><h5>
<a name="id642959"></a>
<a name="id886382"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
Functions</a>
</h5>
@@ -91,7 +91,7 @@
Accessor function returns the lambda parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a><h5>
<a name="id643101"></a>
<a name="id886483"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -111,7 +111,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a><h5>
<a name="id643272"></a>
<a name="id886583"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -122,7 +122,7 @@
should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a><h5>
<a name="id643350"></a>
<a name="id886631"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
</h5>
<p>
@@ -283,7 +283,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a><h5>
<a name="id643652"></a>
<a name="id886881"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -310,8 +310,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

15
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Extreme Value Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="exp_dist.html" title="Exponential Distribution">
@@ -100,7 +100,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/extreme_value_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a><h5>
<a name="id644410"></a>
<a name="id887520"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
Functions</a>
</h5>
@@ -125,7 +125,7 @@
Returns the scale parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a><h5>
<a name="id644635"></a>
<a name="id887676"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -145,7 +145,7 @@
The domain of the random parameter is [-&#8734;, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a><h5>
<a name="id644805"></a>
<a name="id887774"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -154,7 +154,7 @@
very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a><h5>
<a name="id644859"></a>
<a name="id887807"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
</h5>
<p>
@@ -320,8 +320,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

17
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>F Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="extreme_dist.html" title="Extreme Value Distribution">
@@ -80,7 +80,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/fisher_f_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a><h5>
<a name="id645818"></a>
<a name="id888556"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
Functions</a>
</h5>
@@ -106,7 +106,7 @@
Returns the denominator degrees of freedom parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a><h5>
<a name="id646031"></a>
<a name="id888710"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -126,7 +126,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a><h5>
<a name="id646202"></a>
<a name="id888809"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
</h5>
<p>
@@ -134,7 +134,7 @@
are available illustrating the use of the F Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a><h5>
<a name="id646242"></a>
<a name="id888831"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -143,7 +143,7 @@
refer to those functions for accuracy data.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a><h5>
<a name="id646291"></a>
<a name="id888857"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
</h5>
<p>
@@ -423,8 +423,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

21
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html vendored
View File

@@ -3,11 +3,11 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Gamma (and Erlang) Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="f_dist.html" title="F Distribution">
<link rel="next" href="lognormal_dist.html" title="Log Normal Distribution">
<link rel="next" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
@@ -137,7 +137,7 @@
than a dedicated Erlang Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a><h5>
<a name="id647722"></a>
<a name="id890597"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
Functions</a>
</h5>
@@ -162,7 +162,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a><h5>
<a name="id647926"></a>
<a name="id890743"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -182,7 +182,7 @@
The domain of the random variable is [0,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a><h5>
<a name="id648097"></a>
<a name="id890840"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -194,7 +194,7 @@
refer to the accuracy data for those functions for more information.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a><h5>
<a name="id648166"></a>
<a name="id890878"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
</h5>
<p>
@@ -363,8 +363,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
@@ -372,7 +373,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

344
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html vendored Normal file
View File

@@ -0,0 +1,344 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Hypergeometric Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
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</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist"></a><a class="link" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
Hypergeometric Distribution</a>
</h5></div></div></div>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">hypergeometric</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">hypergeometric_distribution</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">hypergeometric_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Construct:
</span> <span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span>
<span class="comment">// Accessors:
</span> <span class="keyword">unsigned</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="keyword">unsigned</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="keyword">unsigned</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">typedef</span> <span class="identifier">hypergeometric_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">hypergeometric</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<p>
The hypergeometric distribution describes the number of "events"
<span class="emphasis"><em>k</em></span> from a sample <span class="emphasis"><em>n</em></span> drawn from
a total population <span class="emphasis"><em>N</em></span> <span class="emphasis"><em>without replacement</em></span>.
</p>
<p>
Imagine we have a sample of <span class="emphasis"><em>N</em></span> objects of which
<span class="emphasis"><em>r</em></span> are "defective" and N-r are "not
defective" (the terms "success/failure" or "red/blue"
are also used). If we sample <span class="emphasis"><em>n</em></span> items <span class="emphasis"><em>without
replacement</em></span> then what is the probability that exactly <span class="emphasis"><em>k</em></span>
items in the sample are defective? The answer is given by the pdf of
the hypergeometric distribution <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">k</span><span class="special">;</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">N</span><span class="special">)</span></code>, whilst the probability of <span class="emphasis"><em>k</em></span>
defectives or fewer is given by F(k; r, n, N), where F(k) is the CDF
of the hypergeometric distribution.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
Unlike almost all of the other distributions in this library, the hypergeometric
distribution is strictly discrete: it can not be extended to real valued
arguments of its parameters or random variable.
</p></td></tr>
</table></div>
<p>
The following graph shows how the distribution changes as the proportion
of "defective" items changes, while keeping the population
and sample sizes constant:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/hypergeometric_pdf_1.png" align="middle"></span>
</p>
<p>
Note that since the distribution is symmetrical in parameters <span class="emphasis"><em>n</em></span>
and <span class="emphasis"><em>r</em></span>, if we change the sample size and keep the
population and proportion "defective" the same then we obtain
basically the same graphs:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/hypergeometric_pdf_2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a><h5>
<a name="id891735"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span>
</pre>
<p>
Constructs a hypergeometric distribution with with a population of <span class="emphasis"><em>N</em></span>
objects, of which <span class="emphasis"><em>r</em></span> are defective, and from which
<span class="emphasis"><em>n</em></span> are sampled.
</p>
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the total number of objects <span class="emphasis"><em>N</em></span>.
</p>
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the number of objects <span class="emphasis"><em>r</em></span> in population <span class="emphasis"><em>N</em></span>
which are defective.
</p>
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the number of objects <span class="emphasis"><em>n</em></span> which are sampled
from the population <span class="emphasis"><em>N</em></span>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a><h5>
<a name="id891914"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
accessor functions</a> that are generic to all distributions are supported:
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
<a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
<a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
<a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
<a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
<a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
</p>
<p>
The domain of the random variable is the unsigned integers in the range
[max(0, n + r - N), min(n, r)]. A <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
is raised if the random variable is outside this range, or is not an
integral value.
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top">
<p>
The quantile function will by default return an integer result that
has been <span class="emphasis"><em>rounded outwards</em></span>. That is to say lower
quantiles (where the probability is less than 0.5) are rounded downward,
and upper quantiles (where the probability is greater than 0.5) are
rounded upwards. This behaviour ensures that if an X% quantile is requested,
then <span class="emphasis"><em>at least</em></span> the requested coverage will be present
in the central region, and <span class="emphasis"><em>no more than</em></span> the requested
coverage will be present in the tails.
</p>
<p>
This behaviour can be changed so that the quantile functions are rounded
differently using <a class="link" href="../../../policy/pol_overview.html" title="Policy Overview">Policies</a>.
It is strongly recommended that you read the tutorial <a class="link" href="../../../policy/pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
Quantiles of Discrete Distributions</a> before using the quantile
function on the Hypergeometric distribution. The <a class="link" href="../../../policy/pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
docs</a> describe how to change the rounding policy for these distributions.
</p>
<p>
However, note that the implementation method of the quantile function
always returns an integral value, therefore attempting to use a <a class="link" href="../../../policy.html" title="Policies">Policy</a> that requires (or produces)
a real valued result will result in a compile time error.
</p>
</td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a><h5>
<a name="id892064"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>
</h5>
<p>
For small N such that <code class="computeroutput"><span class="identifier">N</span> <span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_factorial</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">value</span></code>
then table based lookup of the results gives an accuracy to a few epsilon.
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_factorial</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">value</span></code> is 170 at double or long double
precision.
</p>
<p>
For larger N such that <code class="computeroutput"><span class="identifier">N</span> <span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">prime</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_prime</span><span class="special">)</span></code> then only basic arithmetic is required
for the calculation and the accuracy is typically &lt; 20 epsilon. This
takes care of N up to 104729.
</p>
<p>
For <code class="computeroutput"><span class="identifier">N</span> <span class="special">&gt;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">prime</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">max_prime</span><span class="special">)</span></code>
then accuracy quickly degrades, with 5 or 6 decimal digits being lost
for N = 110000.
</p>
<p>
In general for very large N, the user should expect to loose log<sub>10</sub>N decimal
digits of precision during the calculation, with the results becoming
meaningless for N &gt;= 10<sup>15</sup>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a><h5>
<a name="id893952"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>
</h5>
<p>
There are three sets of tests: our implementation is tested against a
table of values produced by Mathematica's implementation of this distribution.
We also sanity check our implementation against some spot values computed
using the online calculator here <a href="http://stattrek.com/Tables/Hypergeometric.aspx" target="_top">http://stattrek.com/Tables/Hypergeometric.aspx</a>.
Finally we test accuracy against some high precision test data using
this implementation and NTL::RR.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a><h5>
<a name="id893976"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>
</h5>
<p>
The PDF can be calculated directly using the formula:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric1.png"></span>
</p>
<p>
However, this can only be used directly when the largest of the factorials
is guaranteed not to overflow the floating point representation used.
This formula is used directly when <code class="computeroutput"><span class="identifier">N</span>
<span class="special">&lt;</span> <span class="identifier">max_factorial</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;::</span><span class="identifier">value</span></code>
in which case table lookup of the factorials gives a rapid and accurate
implementation method.
</p>
<p>
For larger <span class="emphasis"><em>N</em></span> the method described in "An Accurate
Computation of the Hypergeometric Distribution Function", Trong
Wu, ACM Transactions on Mathematical Software, Vol. 19, No. 1, March
1993, Pages 33-43 is used. The method relies on the fact that there is
an easy method for factorising a factorial into the product of prime
numbers:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric2.png"></span>
</p>
<p>
Where p<sub>i</sub> is the i'th prime number, and e<sub>i</sub> is a small positive integer or
zero, which can be calculated via:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric3.png"></span>
</p>
<p>
Further we can combine the factorials in the expression for the PDF to
yield the PDF directly as the product of prime numbers:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric4.png"></span>
</p>
<p>
With this time the exponents e<sub>i</sub> being either positive, negative or zero.
Indeed such a degree of cancellation occurs in the calculation of the
e<sub>i</sub> that many are zero, and typically most have a magnitude or no more
than 1 or 2.
</p>
<p>
Calculation of the product of the primes requires some care to prevent
numerical overflow, we use a novel recursive method which splits the
calculation into a series of sub-products, with a new sub-product started
each time the next multiplication would cause either overflow or underflow.
The sub-products are stored in a linked list on the program stack, and
combined in an order that will guarantee no overflow or unnecessary-underflow
once the last sub-product has been calculated.
</p>
<p>
This method can be used as long as N is smaller than the largest prime
number we have stored in our table of primes (currently 104729). The
method is relatively slow (calculating the exponents requires the most
time), but requires only a small number of arithmetic operations to calculate
the result (indeed there is no shorter method involving only basic arithmetic
once the exponents have been found), the method is therefore much more
accurate than the alternatives.
</p>
<p>
For much larger N, we can calculate the PDF from the factorials using
either lgamma, or by directly combining lanczos approximations to avoid
calculating via logarithms. We use the latter method, as it is usually
1 or 2 decimal digits more accurate than computing via logarithms with
lgamma. However, in this area where N &gt; 104729, the user should expect
to loose around log<sub>10</sub>N decimal digits during the calculation in the worst
case.
</p>
<p>
The CDF and its complement is calculated by directly summing the PDF's.
We start by deciding whether the CDF, or its complement, is likely to
be the smaller of the two and then calculate the PDF at <span class="emphasis"><em>k</em></span>
(or <span class="emphasis"><em>k+1</em></span> if we're calculating the complement) and
calculate successive PDF values via the recurrence relations:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric5.png"></span>
</p>
<p>
Until we either reach the end of the distributions domain, or the next
PDF value to be summed would be too small to affect the result.
</p>
<p>
The quantile is calculated in a similar manner to the CDF: we first guess
which end of the distribution we're nearer to, and then sum PDFs starting
from the end of the distribution this time, until we have some value
<span class="emphasis"><em>k</em></span> that gives the required CDF.
</p>
<p>
The median is simply the quantile at 0.5, and the remaining properties
are calculated via:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/hypergeometric6.png"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist"></a><a class="link" href="laplace_dist.html" title="Laplace Distribution"> Laplace
Distribution</a>
</h5></div></div></div>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">laplace</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">laplace_distribution</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">laplace_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">laplace</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">laplace_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Construct:
</span> <span class="identifier">laplace_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
<span class="comment">// Accessors:
</span> <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<p>
Laplace distribution is the distribution of differences between two independent
variates with identical exponential distributions (Abramowitz and Stegun
1972, p. 930). It is also called the double exponential distribution.
</p>
<p>
For location parameter &#956; and scale parameter &#963; it is defined by the probability
density function:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/laplace_pdf.png"></span>
</p>
<p>
The location and scale parameters are equivalent to the mean and standard
deviation of the normal or Gaussian distribution.
</p>
<p>
The following graph illustrates the effect of the location parameter
&#956; on the PDF. Note that the range of the random variable remains [-&#8734;,+&#8734;]
irrespective of the value of the location parameter:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/laplace_pdf_mu.png" align="middle"></span>
</p>
<p>
The next graph illustrates the effect of the scale parameter &#963; on the PDF:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/laplace_pdf_sigma.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a><h5>
<a name="id894733"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">laplace_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
</pre>
<p>
Constructs a laplace distribution with location <span class="emphasis"><em>location</em></span>
and scale <span class="emphasis"><em>scale</em></span>.
</p>
<p>
The location parameter is the same as the mean of the random variate.
</p>
<p>
The scale parameter is proportional to the standard deviation of the
random variate.
</p>
<p>
Requires that the scale parameter is greater than zero, otherwise calls
<a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the <span class="emphasis"><em>location</em></span> parameter of this distribution.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a><h5>
<a name="id894895"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
accessor functions</a> that are generic to all distributions are supported:
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
<a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
<a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
<a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
<a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
<a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
</p>
<p>
The domain of the random variable is [-&#8734;,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a><h5>
<a name="id894992"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>
</h5>
<p>
The laplace distribution is implemented in terms of the standard library
log and exp functions and as such should have very small errors.
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a><h5>
<a name="id895011"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>
</h5>
<p>
In the following table &#956; is the location parameter of the distribution,
&#963; is its scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
<span class="emphasis"><em>p</em></span> is the probability and its complement <span class="emphasis"><em>q
= 1-p</em></span>.
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-abs(x-&#956;) / &#963;</sup> / (2 * &#963;)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
x &lt; &#956; : p = e<sup>(x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
x &gt;= &#956; : p = 1 - e<sup>(&#956;-x)/&#963; </sup> / &#963;
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
-x &lt; &#956; : q = e<sup>(-x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
-x &gt;= &#956; : q = 1 - e<sup>(&#956;+x)/&#963; </sup> / &#963;
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
p &lt; 0.5 : x = &#956; + &#963; * log(2*p)
</p>
<p>
p &gt;= 0.5 : x = &#956; - &#963; * log(2-2*p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
q &gt; 0.5: x = &#956; + &#963;*log(2-2*q)
</p>
<p>
q &lt;=0.5: x = &#956; - &#963;*log( 2*q )
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
</td>
<td>
<p>
&#956;
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
</td>
<td>
<p>
2 * &#963;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
</td>
<td>
<p>
&#956;
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
</td>
<td>
<p>
6
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
3
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a><h5>
<a name="id895320"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<a href="http://mathworld.wolfram.com/LaplaceDistribution.html" target="_top">Weisstein,
Eric W. "Laplace Distribution."</a> From MathWorld--A
Wolfram Web Resource.
</li>
<li><a href="http://en.wikipedia.org/wiki/Laplace_distribution" target="_top">Laplace
Distribution</a></li>
<li>
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,
1972, p. 930.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">
Logistic Distribution</a>
</h5></div></div></div>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">logistic</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">logistic_distribution</span><span class="special">;</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">logistic_distribution</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
<span class="comment">// Construct:
</span> <span class="identifier">logistic_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
<span class="comment">// Accessors:
</span> <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// location.
</span> <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> <span class="comment">// scale.
</span>
<span class="special">};</span>
<span class="keyword">typedef</span> <span class="identifier">logistic_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">logistic</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<p>
The logistic distribution is a continous probability distribution. It
has two parameters - location and scale. The cumulative distribution
function of the logistic distribution appears in logistic regression
and feedforward neural networks. Among other applications, United State
Chess Federation and FIDE use it to calculate chess ratings.
</p>
<p>
The following graph shows how the distribution changes as the parameters
change:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/logistic_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>
<a name="id895799"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">logistic_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">u</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">s</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
</pre>
<p>
Constructs a logistic distribution with location <span class="emphasis"><em>u</em></span>
and scale <span class="emphasis"><em>s</em></span>.
</p>
<p>
Requires <code class="computeroutput"><span class="identifier">scale</span> <span class="special">&gt;</span>
<span class="number">0</span></code>, otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
is raised.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the location of this distribution.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the scale of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>
<a name="id895964"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
<p>
All the <a class="link" href="../nmp.html" title="Non-Member Properties">usual non-member
accessor functions</a> that are generic to all distributions are supported:
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>,
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>, <a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link" href="../nmp.html#math.dist.hazard">Hazard
Function</a>, <a class="link" href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,
<a class="link" href="../nmp.html#math.dist.mean">mean</a>, <a class="link" href="../nmp.html#math.dist.median">median</a>,
<a class="link" href="../nmp.html#math.dist.mode">mode</a>, <a class="link" href="../nmp.html#math.dist.variance">variance</a>,
<a class="link" href="../nmp.html#math.dist.sd">standard deviation</a>, <a class="link" href="../nmp.html#math.dist.skewness">skewness</a>,
<a class="link" href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link" href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,
<a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
</p>
<p>
The domain of the random variable is [-[max_value], +[min_value]]. However,
the pdf and cdf support inputs of +&#8734; and -&#8734;
as special cases if RealType
permits.
</p>
<p>
At <code class="computeroutput"><span class="identifier">p</span><span class="special">=</span><span class="number">1</span></code> and <code class="computeroutput"><span class="identifier">p</span><span class="special">=</span><span class="number">0</span></code>, the
quantile function returns the result of +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>
and -<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>, while the
complement quantile function returns the result of -<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>
and +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a> respectively.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
<a name="id896855"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
</h5>
<p>
The logistic distribution is implemented in terms of the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code> and the <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span></code>
functions, so its accuracy is related to the accurate implementations
of those functions on a given platform. When calculating the quantile
with a non-zero <span class="emphasis"><em>position</em></span> parameter catastrophic
cancellation errors can occur: in such cases, only a low <span class="emphasis"><em>absolute
error</em></span> can be guarenteed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>
<a name="id896910"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>
</h5>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-(x-u)/s</sup> / (s*(1+e<sup>-(x-u)/s</sup>)<sup>2</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = 1/(1+e<sup>-(x-u)/s</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 1/(1+e<sup>(x-u)/s</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = u - s*log(1/p-1)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = u + s*log(p/1-p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
</td>
<td>
<p>
u
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
</td>
<td>
<p>
The same as the mean.
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
6/5
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
</td>
<td>
<p>
(&#960;*s)<sup>2</sup> / 3
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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<a accesskey="p" href="laplace_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
</body>
</html>

21
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html vendored
View File

@@ -3,10 +3,10 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Log Normal Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
<link rel="prev" href="logistic_dist.html" title="Logistic Distribution">
<link rel="next" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -20,7 +20,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h5 class="title">
@@ -88,7 +88,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/lognormal_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a><h5>
<a name="id649215"></a>
<a name="id897646"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
Functions</a>
</h5>
@@ -121,7 +121,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a><h5>
<a name="id649442"></a>
<a name="id897806"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -141,7 +141,7 @@
The domain of the random variable is [0,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a><h5>
<a name="id649610"></a>
<a name="id897905"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -150,7 +150,7 @@
function</a>, and as such should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a><h5>
<a name="id649651"></a>
<a name="id897933"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
</h5>
<p>
@@ -318,8 +318,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
@@ -327,7 +328,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
</body>
</html>

19
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Noncentral Beta Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
@@ -96,7 +96,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_beta_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a><h5>
<a name="id655529"></a>
<a name="id903572"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
Functions</a>
</h5>
@@ -128,7 +128,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a><h5>
<a name="id655786"></a>
<a name="id903758"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -152,7 +152,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
The domain of the random variable is [0, 1].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a><h5>
<a name="id655960"></a>
<a name="id903859"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -168,7 +168,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
zero error</a>.
</p>
<div class="table">
<a name="id656022"></a><p class="title"><b>Table 13. Errors In CDF of the Noncentral Beta</b></p>
<a name="id903894"></a><p class="title"><b>Table 13. Errors In CDF of the Noncentral Beta</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Beta">
<colgroup>
<col>
@@ -295,7 +295,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
functions are broadly similar.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a><h5>
<a name="id656232"></a>
<a name="id904077"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
</h5>
<p>
@@ -307,7 +307,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
tests.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a><h5>
<a name="id656275"></a>
<a name="id904101"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
</h5>
<p>
@@ -398,8 +398,9 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

21
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Noncentral Chi-Squared Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
@@ -110,7 +110,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/nccs_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a><h5>
<a name="id657715"></a>
<a name="id905705"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions">Member
Functions</a>
</h5>
@@ -183,7 +183,7 @@
<span class="special">==</span> <span class="identifier">q</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a><h5>
<a name="id658951"></a>
<a name="id906606"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -203,7 +203,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a><h5>
<a name="id659123"></a>
<a name="id906706"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
</h5>
<p>
@@ -211,7 +211,7 @@
example</a> for the noncentral chi-squared distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a><h5>
<a name="id659162"></a>
<a name="id906733"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -223,7 +223,7 @@
zero error</a>.
</p>
<div class="table">
<a name="id659210"></a><p class="title"><b>Table 14. Errors In CDF of the Noncentral Chi-Squared</b></p>
<a name="id906763"></a><p class="title"><b>Table 14. Errors In CDF of the Noncentral Chi-Squared</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Chi-Squared">
<colgroup>
<col>
@@ -359,7 +359,7 @@
produce an accuracy greater than the square root of the machine epsilon.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a><h5>
<a name="id659445"></a>
<a name="id906961"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
</h5>
<p>
@@ -373,7 +373,7 @@
to at least 50 decimal digits - and is the used for our accuracy tests.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a><h5>
<a name="id659498"></a>
<a name="id906980"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
@@ -500,8 +500,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

17
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Noncentral F Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
@@ -95,7 +95,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_f_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a><h5>
<a name="id660737"></a>
<a name="id908176"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
Functions</a>
</h5>
@@ -127,7 +127,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
which this object was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a><h5>
<a name="id660995"></a>
<a name="id908364"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -147,7 +147,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a><h5>
<a name="id661167"></a>
<a name="id908464"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -155,7 +155,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
Beta Distribution</a>: refer to that distribution for accuracy data.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a><h5>
<a name="id661207"></a>
<a name="id908488"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
</h5>
<p>
@@ -164,7 +164,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
Math library statistical package</a> and its pbeta and dbeta functions.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a><h5>
<a name="id661245"></a>
<a name="id908512"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
</h5>
<p>
@@ -407,8 +407,9 @@ is the non-centrality parameter, <span class="emphasis"><em>x</em></span> is the
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

19
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Noncentral T Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_f_dist.html" title="Noncentral F Distribution">
@@ -85,7 +85,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_t_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a><h5>
<a name="id662409"></a>
<a name="id909390"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
Functions</a>
</h5>
@@ -111,7 +111,7 @@
which this object was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a><h5>
<a name="id662603"></a>
<a name="id909530"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -131,7 +131,7 @@
The domain of the random variable is [-&#8734;, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a><h5>
<a name="id662775"></a>
<a name="id909629"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -141,7 +141,7 @@
one shown will have <a class="link" href="../../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
</p>
<div class="table">
<a name="id662815"></a><p class="title"><b>Table 15. Errors In CDF of the Noncentral T Distribution</b></p>
<a name="id909652"></a><p class="title"><b>Table 15. Errors In CDF of the Noncentral T Distribution</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral T Distribution">
<colgroup>
<col>
@@ -255,7 +255,7 @@
epsilon.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a><h5>
<a name="id663009"></a>
<a name="id909810"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
</h5>
<p>
@@ -270,7 +270,7 @@
least 50 decimal places.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a><h5>
<a name="id663051"></a>
<a name="id909830"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
</h5>
<p>
@@ -351,8 +351,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

31
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Negative Binomial Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="lognormal_dist.html" title="Log Normal Distribution">
@@ -123,7 +123,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/negative_binomial_pdf_2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a><h5>
<a name="id651123"></a>
<a name="id899065"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
Distributions</a>
</h5>
@@ -200,12 +200,12 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a><h5>
<a name="id651327"></a>
<a name="id899175"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct"></a><h6>
<a name="id651354"></a>
<a name="id899189"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
@@ -221,7 +221,7 @@
<span class="special">&lt;=</span> <span class="number">1</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
<a name="id651509"></a>
<a name="id899298"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// successes / trials (0 &lt;= p &lt;= 1)
@@ -237,7 +237,7 @@
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a><h6>
<a name="id651635"></a>
<a name="id899383"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p">Lower
Bound on Parameter p</a>
</h6>
@@ -298,7 +298,7 @@
vol. 48, no3, 605-621</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a><h6>
<a name="id651999"></a>
<a name="id899647"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p">Upper
Bound on Parameter p</a>
</h6>
@@ -358,7 +358,7 @@
vol. 48, no3, 605-621</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a><h6>
<a name="id652360"></a>
<a name="id899907"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
Number of Trials to Ensure at Least a Certain Number of Failures</a>
</h6>
@@ -409,7 +409,7 @@
probability of observing k failures or fewer.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a><h6>
<a name="id652667"></a>
<a name="id900128"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
Number of Trials to Ensure a Maximum Number of Failures or Less</a>
</h6>
@@ -457,7 +457,7 @@
probability of observing more than k failures.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a><h5>
<a name="id652984"></a>
<a name="id900356"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -478,7 +478,7 @@
in the context of this distribution:
</p>
<div class="table">
<a name="id653148"></a><p class="title"><b>Table 12. Meaning of the non-member accessors.</b></p>
<a name="id900450"></a><p class="title"><b>Table 12. Meaning of the non-member accessors.</b></p>
<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors.">
<colgroup>
<col>
@@ -603,7 +603,7 @@
</table></div>
</div>
<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
<a name="id653706"></a>
<a name="id900861"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -613,7 +613,7 @@
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a><h5>
<a name="id653756"></a>
<a name="id900888"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
</h5>
<p>
@@ -894,8 +894,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

15
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_t_dist.html" title="Noncentral T Distribution">
@@ -79,7 +79,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/normal_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a><h5>
<a name="id664056"></a>
<a name="id911876"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
Functions</a>
</h5>
@@ -109,7 +109,7 @@
be used generically).
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a><h5>
<a name="id664330"></a>
<a name="id912071"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -131,7 +131,7 @@
and complement cdf -&#8734; = 1 and +&#8734; = 0, if RealType permits.
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a><h5>
<a name="id664507"></a>
<a name="id912168"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -139,7 +139,7 @@
function</a>, and as such should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a><h5>
<a name="id664547"></a>
<a name="id912194"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
</h5>
<p>
@@ -289,8 +289,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

74
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Pareto Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="normal_dist.html" title="Normal (Gaussian) Distribution">
@@ -33,9 +33,9 @@
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">pareto</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span> <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span>
<span class="keyword">class</span> <a class="link" href="../../../policy.html" title="Policies">Policy</a> <span class="special">=</span> <a class="link" href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy Class Reference">policies::policy&lt;&gt;</a> <span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">pareto_distribution</span><span class="special">;</span>
@@ -47,9 +47,9 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="comment">// Constructor:
</span> <span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
</span> <span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">)</span>
<span class="comment">// Accessors:
</span> <span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</span> <span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<span class="special">};</span>
@@ -64,16 +64,17 @@
f(x; &#945;, &#946;) = &#945;&#946;<sup>&#945;</sup> / x<sup>&#945;+ 1</sup>
</p>
<p>
For shape parameter &#945; &gt; 0, and location parameter &#946; &gt; 0, and &#945; &gt; 0.
For shape parameter &#945; &gt; 0, and scale parameter &#946; &gt; 0. If x &lt; &#946;, the
pdf is zero.
</p>
<p>
The <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Pareto
The <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Pareto
distribution</a> often describes the larger compared to the smaller.
A classic example is that 80% of the wealth is owned by 20% of the population.
</p>
<p>
The following graph illustrates how the PDF varies with the location
parameter &#946;:
The following graph illustrates how the PDF varies with the scale parameter
&#946;:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf1.png" align="middle"></span>
@@ -86,16 +87,16 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
<a name="id665570"></a>
<a name="id912966"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.related_distributions">Related
distributions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions"></a><h5>
<a name="id665595"></a>
<a name="id912984"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
Functions</a>
</h5>
<pre class="programlisting"><span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">location</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
<pre class="programlisting"><span class="identifier">pareto_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">shape</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span>
</pre>
<p>
Constructs a <a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">pareto
@@ -106,10 +107,10 @@
Requires that the <span class="emphasis"><em>shape</em></span> and <span class="emphasis"><em>scale</em></span>
parameters are both greater than zero, otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">location</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">scale</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Returns the <span class="emphasis"><em>location</em></span> parameter of this distribution.
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">shape</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
</pre>
@@ -117,7 +118,7 @@
Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
<a name="id665825"></a>
<a name="id913152"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -134,25 +135,28 @@
<a class="link" href="../nmp.html#math.dist.range">range</a> and <a class="link" href="../nmp.html#math.dist.support">support</a>.
</p>
<p>
The supported domain of the random variable is [location, &#8734;].
The supported domain of the random variable is [scale, &#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
<a name="id665997"></a>
<a name="id913252"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
</h5>
<p>
The pareto distribution is implemented in terms of the standard library
<code class="computeroutput"><span class="identifier">exp</span></code> functions plus <a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a> and as such
should have very low error rates except when probability is very close
to unity.
The Pareto distribution is implemented in terms of the standard library
<code class="computeroutput"><span class="identifier">exp</span></code> functions plus <a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a> and so should
have very small errors, usually only a few epsilon.
</p>
<p>
If probability is near to unity (or the complement of a probability near
zero) see also <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why complements?</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a><h5>
<a name="id666051"></a>
<a name="id913289"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
</h5>
<p>
In the following table &#945; is the shape parameter of the distribution, and
&#946; is its location parameter, <span class="emphasis"><em>x</em></span> is the random variate,
&#946; is its scale parameter, <span class="emphasis"><em>x</em></span> is the random variate,
<span class="emphasis"><em>p</em></span> is the probability and its complement <span class="emphasis"><em>q
= 1-p</em></span>.
</p>
@@ -218,7 +222,7 @@
</td>
<td>
<p>
Using the relation: x = &#945; / (1 - p)<sup>1/&#946;</sup>
Using the relation: x = &#946; / (1 - p)<sup>1/&#945;</sup>
</p>
</td>
</tr>
@@ -230,7 +234,7 @@
</td>
<td>
<p>
Using the relation: x = &#945; / (q)<sup>1/&#946;</sup>
Using the relation: x = &#946; / (q)<sup>1/&#945;</sup>
</p>
</td>
</tr>
@@ -278,7 +282,7 @@
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
@@ -292,7 +296,7 @@
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
@@ -306,7 +310,7 @@
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
@@ -315,7 +319,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
<a name="id666407"></a>
<a name="id913601"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -324,12 +328,18 @@
<li><a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<li>
Handbook of Statistical Distributions with Applications, K Krishnamoorthy,
ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of
a and b is reversed in Wolfram and Krishnamoorthy).
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

15
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Poisson Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="pareto.html" title="Pareto Distribution">
@@ -122,7 +122,7 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a><h5>
<a name="id667162"></a>
<a name="id914123"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
Functions</a>
</h5>
@@ -137,7 +137,7 @@
Returns the <span class="emphasis"><em>mean</em></span> of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
<a name="id667286"></a>
<a name="id914212"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -157,7 +157,7 @@
The domain of the random variable is [0, &#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
<a name="id667455"></a>
<a name="id914309"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -171,7 +171,7 @@
using an iterative method with a lower tolerance to avoid excessive computation.
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a><h5>
<a name="id667504"></a>
<a name="id914338"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
</h5>
<p>
@@ -326,8 +326,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

19
doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html vendored
View File

@@ -3,7 +3,7 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Rayleigh Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="poisson_dist.html" title="Poisson Distribution">
@@ -86,7 +86,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/rayleigh_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a><h5>
<a name="id668443"></a>
<a name="id915045"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
distributions</a>
</h5>
@@ -102,7 +102,7 @@
distribution</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a><h5>
<a name="id668519"></a>
<a name="id915096"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
Functions</a>
</h5>
@@ -121,7 +121,7 @@
Returns the <span class="emphasis"><em>sigma</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a><h5>
<a name="id668666"></a>
<a name="id915200"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -141,7 +141,7 @@
The domain of the random variable is [0, max_value].
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a><h5>
<a name="id668836"></a>
<a name="id915299"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
</h5>
<p>
@@ -151,7 +151,7 @@
using NTL RR type with 150-bit accuracy, about 50 decimal digits.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a><h5>
<a name="id668893"></a>
<a name="id915333"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
</h5>
<p>
@@ -320,7 +320,7 @@
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a><h5>
<a name="id669282"></a>
<a name="id916643"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
@@ -332,8 +332,9 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
Holin, Xiaogang Zhang, Bruno Lalande and Johan Råde<p>
<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani
and Thijs van den Berg<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>

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