From b11ef8b992dc6f5df23182561d1d10e07eed9af1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 16 Oct 2011 18:57:30 +0000 Subject: [PATCH] Merge recent bug fixes from Trunk. Refs #6014 Refs #5832 Refs #5934 Refs #6001 Refs #5982 Refs #5914 Refs #5927 [SVN r74984] --- doc/sf_and_dist/html/index.html | 15 +- doc/sf_and_dist/html/index/s12.html | 2649 ++++---- doc/sf_and_dist/html/index/s13.html | 173 +- doc/sf_and_dist/html/index/s14.html | 381 +- doc/sf_and_dist/html/index/s15.html | 271 +- doc/sf_and_dist/html/index/s16.html | 5883 +++++++++-------- .../html/math_toolkit/backgrounders.html | 9 +- .../backgrounders/implementation.html | 77 +- .../math_toolkit/backgrounders/lanczos.html | 39 +- .../html/math_toolkit/backgrounders/refs.html | 19 +- .../backgrounders/relative_error.html | 11 +- .../math_toolkit/backgrounders/remez.html | 51 +- doc/sf_and_dist/html/math_toolkit/dist.html | 11 +- .../html/math_toolkit/dist/dist_ref.html | 9 +- .../dist/dist_ref/dist_algorithms.html | 81 +- .../math_toolkit/dist/dist_ref/dists.html | 9 +- .../dist/dist_ref/dists/bernoulli_dist.html | 41 +- .../dist/dist_ref/dists/beta_dist.html | 123 +- 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.../boost/math/special_functions/trunc.hpp | 10 +- include/boost/math/tools/config.hpp | 2 +- include/boost/math/tools/toms748_solve.hpp | 2 +- include/boost/math/tools/tuple.hpp | 2 +- octonion/octonion_test.cpp | 122 +- quaternion/quaternion_mult_incl_test.cpp | 19 +- quaternion/quaternion_test.cpp | 111 +- special_functions/acosh_test.hpp | 10 +- special_functions/asinh_test.hpp | 10 +- special_functions/atanh_test.hpp | 15 +- special_functions/sinc_test.hpp | 12 +- special_functions/sinhc_test.hpp | 12 +- special_functions/special_functions_test.cpp | 28 +- test/acosh_test.hpp | 12 +- test/asinh_test.hpp | 12 +- test/atanh_test.hpp | 19 +- test/common_factor_test.cpp | 1 - test/complex_test.cpp | 8 +- test/sinc_test.hpp | 14 +- test/sinhc_test.hpp | 14 +- test/special_functions_test.cpp | 27 +- test/test_next.cpp | 18 + test/test_round.cpp | 68 +- test/test_signed_zero.cpp | 2 +- 303 files changed, 9433 insertions(+), 9472 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index c21acde39..336e29ddb 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -3,7 +3,7 @@ Math Toolkit - + @@ -18,7 +18,7 @@
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Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg

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+

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)

@@ -104,7 +103,7 @@ are Objects
Generic operations common to all distributions are non-member functions
-
Complements +
Complements are supported too - and when to use them
Parameters can be calculated
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Last revised: July 16, 2011 at 10:40:56 GMT

Last revised: October 13, 2011 at 15:53:36 GMT
diff --git a/doc/sf_and_dist/html/index/s12.html b/doc/sf_and_dist/html/index/s12.html index 35703b934..8746703c6 100644 --- a/doc/sf_and_dist/html/index/s12.html +++ b/doc/sf_and_dist/html/index/s12.html @@ -3,7 +3,7 @@ Function Index - + @@ -22,2232 +22,2233 @@
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+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index f4988cade..09290a097 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -3,7 +3,7 @@ Class Index - + @@ -22,210 +22,209 @@
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+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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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Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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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+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index b6118ef6a..19d5c0c7f 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -3,7 +3,7 @@ Index - + @@ -21,4470 +21,4473 @@
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+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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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Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index 19c674afe..65cc3caf2 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -3,7 +3,7 @@ Additional Implementation Notes - + @@ -22,7 +22,7 @@
PrevUpHomeNext
-
+

Additional Implementation Notes @@ -33,7 +33,7 @@ and reflect more the general implementation philosophy used.

- + Implemention philosophy
@@ -85,7 +85,7 @@ These could still provide sufficient accuracy for some speed-critical applications.

- + Accuracy and Representation of Test Values
@@ -130,18 +130,18 @@ binary value).

- + Tolerance of Tests

The tolerances need to be set to the maximum of:

-
    -
  • +
      +
    • Some epsilon value.
      • -
    • +
    • The accuracy of the data (often only near 64-bit double).
    @@ -156,7 +156,7 @@ first that the suffix L is present, and then that the tolerance is big enough.

    - + Handling Unsuitable Arguments
    @@ -166,7 +166,7 @@ it is proposed that signalling a domain error is mandatory when the argument would give an mathematically undefined result.

    -
    • +
      • Guideline 1

      @@ -183,7 +183,7 @@ a domain error whenever evaluated with argument values for which the mathematical function is undefined.

      -
      • +
        • Guideline 2

        @@ -224,7 +224,7 @@

- + Handling of Functions that are Not Mathematically defined
@@ -258,7 +258,7 @@

- + Median of distributions
@@ -293,7 +293,7 @@ Basic Statistics. give more detail, in particular for discrete distributions.

- + Handling of Floating-Point Infinity
@@ -337,7 +337,7 @@ handling policies.

- + Scale, Shape and Location
@@ -350,8 +350,8 @@ RealType lower = dist.lower(); RealType mode = dist.mode(); RealType upper = dist.upper(); - RealType result; // of checks. - if(false == detail::check_triangular(BOOST_CURRENT_FUNCTION, lower, mode, upper, &result)) + RealType result; // of checks. + if(false == detail::check_triangular(BOOST_CURRENT_FUNCTION, lower, mode, upper, &result)) { return result; } @@ -364,11 +364,11 @@ functions, they can be added if required.

- + Notes on Implementation of Specific Functions & Distributions
-
  • +
    • Default parameters for the Triangular Distribution. We are uncertain about the best default parameters. Some sources suggest that the Standard Triangular Distribution has lower = 0, mode = half and upper = 1. However @@ -376,7 +376,7 @@ lower = -1, mode = 0 and upper = 1 would be more suitable.
    - + Rational Approximations Used
    @@ -419,7 +419,7 @@ to the "true" minimax solution.

    - + Representation of Mathematical Constants
    @@ -471,16 +471,16 @@

    So you cannot write

    -
    double p = boost::math::constants::pi<>();  // could not deduce template argument for 'T'
-
    +
    double p = boost::math::constants::pi<>();  // could not deduce template argument for 'T'
+

    Neither can you write:

    -
    double p = boost::math::constants::pi; // Context does not allow for disambiguation of overloaded function
-double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
-
    +
    double p = boost::math::constants::pi; // Context does not allow for disambiguation of overloaded function
+double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
+
    - + Thread safety
    @@ -505,7 +505,7 @@ the right thing here at some point.

    - + Sources of Test Data
    @@ -546,7 +546,7 @@ the underlying special function is known to be difficult to implement.

    - + Creating and Managing the Equations
    @@ -696,8 +696,8 @@ done <font weight="bold" style="italic"><font-data ttf="palabi.ttf"/></font> </font-family> - <font-family name"Lucida Sans Unicode"> - <!-- <font><font-data ttf"lsansuni.ttf"><font> --> + <font-family name="Lucida Sans Unicode"> + <!-- <font><font-data ttf="lsansuni.ttf"><font> --> <!-- actually called l_10646.ttf on Windows 2000 and Vista Sp1 --> <font><font-data ttf="l_10646.ttf"></font> </font-family> @@ -718,11 +718,11 @@ done template defined in math.qbk. This outputs Docbook XML that looks like: 

    <inlinemediaobject>
-<imageobject role"html">
-<imagedata fileref"../equations/myfile.png"></imagedata>
+<imageobject role="html">
+<imagedata fileref="../equations/myfile.png"></imagedata>
 </imageobject>
-<imageobject role"print">
-<imagedata fileref"../equations/myfile.svg"></imagedata>
+<imageobject role="print">
+<imagedata fileref="../equations/myfile.svg"></imagedata>
 </imageobject>
 </inlinemediaobject>
    @@ -731,7 +731,7 @@ done HTML: this needs further investigation.

    - + Producing Graphs
    @@ -750,9 +750,8 @@ done
-
Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

+

Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index 546ca6a28..8dd7ffeba 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -3,7 +3,7 @@ The Lanczos Approximation - + @@ -22,12 +22,12 @@
PrevUpHomeNext
-
+
- + Motivation

@@ -45,8 +45,8 @@ Lanczos approximation does have a couple of properties that make it worthy of further consideration:

-
    -
  • +
      +
    • The approximation has an easy to compute truncation error that holds for all z > 0. In practice that means we can use the same approximation for all z > 0, and @@ -54,7 +54,7 @@ the truncation error will at worst be bounded by some finite value.
      • -
    • +
    • The approximation has a form that is particularly amenable to analytic manipulation, in particular ratios of gamma or gamma-like functions are particularly easy to compute without resorting to logarithms. @@ -99,7 +99,7 @@ functions divided by large powers into single (simpler) expressions.

      - + The Approximation
      @@ -161,7 +161,7 @@

- + Computing the Coefficients
@@ -205,7 +205,7 @@ multiplied by F as the last step.

- + Choosing the Right Parameters
@@ -535,24 +535,24 @@ is exact, and so isn't used for the gamma function.

- + References
-
    -
  1. - Paul Godfrey, "A +
      +
    1. + Paul Godfrey, "A note on the computation of the convergent Lanczos complex Gamma approximation".
      2. -
    2. - Glendon Ralph Pugh, "An +
    3. + Glendon Ralph Pugh, "An Analysis of the Lanczos Gamma Approximation", PhD Thesis November 2004.
      4. -
    4. +
    5. Viktor T. Toth, "Calculators and the Gamma Function".
      6. -
    6. +
    7. Mathworld, The Lanczos Approximation.
      8. @@ -560,9 +560,8 @@
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html index 03027ba6b..5113285b3 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -3,7 +3,7 @@ References - + @@ -22,12 +22,12 @@
    PrevUpHomeNext
    -
    +
    - + General references
    @@ -98,7 +98,7 @@ Library (version 2), Walter E. Brown

    - + Calculators

    @@ -116,11 +116,11 @@ provided some spot values.

    - http://www.adsciengineering.combpdcalc + http://www.adsciengineering.com/bpdcalc/ Binomial Probability Distribution Calculator.

    - + Other Libraries

    @@ -145,7 +145,7 @@ arithmetic, for evaluating cumulative probability density functions.

    - http://www.softintegration.com/docs/packagechnagstat + http://www.softintegration.com/docs/package/chnagstat/

    NAG @@ -201,9 +201,8 @@

    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html index 5b0f742a5..8be2aa9dc 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html @@ -3,7 +3,7 @@ Relative Error - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -78,7 +78,7 @@ of binary digits. You have been warned!

    - + The Impossibility of Zero Error
    @@ -106,9 +106,8 @@
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html index 2f180a04a..041a476cf 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -3,7 +3,7 @@ The Remez Method - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -65,15 +65,15 @@ yields the smallest maximal value of the error function. Chebyshev showed that there is a unique minimax solution for R(x) that has the following properties:

    -
      -
    • +
        +
      • If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1 coefficients of the polynomial, and maximal value of the error function.
        • -
      • +
      • The error function has N+1 roots, and N+2 extrema (minima and maxima).
        • -
      • +
      • The extrema alternate in sign, and all have the same magnitude.
      @@ -94,7 +94,7 @@ are located!

      - + The Remez Method
      @@ -174,7 +174,7 @@
    - + Remez Step 1
    @@ -205,7 +205,7 @@ to 5.6x10-4.

    - + Remez Step 2
    @@ -234,7 +234,7 @@ In our example we perform multi-point exchange.

    - + Iteration

    @@ -250,7 +250,7 @@ remez-4

    - + Rational Approximations
    @@ -299,7 +299,7 @@ number of terms overall.

    - + Practical Considerations
    @@ -407,7 +407,7 @@ desired minimax solution (5x10-4).

    - + Remez Method Checklist
    @@ -416,18 +416,18 @@ wrong, it is by no means an exhaustive list, but is provided in the hopes that it will prove useful.

    -
      -
    • +
        +
      • Is the function smooth enough? Can it be better separated into a rapidly changing part, and an asymptotic part?
        • -
      • +
      • Does the function being approximated have any "blips" in it? Check for problems as the function changes computation method, or if a root, or an infinity has been divided out. The telltale sign is if there is a narrow region where the Remez method will not converge.
        • -
      • +
      • Check you have enough accuracy in your calculations: remember that the Remez method works on the difference between the approximation and the function being approximated: so you must have more digits of precision @@ -435,33 +435,33 @@ So for example at double precision, you shouldn't expect to be able to get better than a float precision approximation.
        • -
      • +
      • Try skewing the initial interpolated approximation to minimise the error before you begin the Remez steps.
        • -
      • +
      • If the approximation won't converge or is ill-conditioned from one starting location, try starting from a different location.
        • -
      • +
      • If a rational function won't converge, one can minimise a polynomial (which presents no problems), then rotate one term from the numerator to the denominator and minimise again. In theory one can continue moving terms one at a time from numerator to denominator, and then re-minimising, retaining the last set of control points at each stage.
        • -
      • +
      • Try using a smaller interval. It may also be possible to optimise over one (small) interval, rescale the control points over a larger interval, and then re-minimise.
        • -
      • +
      • Keep absissa values small: use a change of variable to keep the abscissa over, say [0, b], for some smallish value b.
      - + References

      @@ -527,9 +527,8 @@

    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index ab5eb8ba6..6e699f706 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -3,7 +3,7 @@ Statistical Distributions and Functions - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -38,7 +38,7 @@ are Objects
    Generic operations common to all distributions are non-member functions
    -
    Complements +
    Complements are supported too - and when to use them
    Parameters can be calculated
    @@ -207,9 +207,8 @@
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html index 6fd5e54a3..d845e147f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html @@ -3,7 +3,7 @@ Statistical Distributions Reference - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 66d061229..a2e2ab52b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -3,7 +3,7 @@ Distribution Algorithms - + @@ -22,13 +22,13 @@
    PrevUpHomeNext
    -
    +
    - + Finding the Location and Scale for Normal and similar distributions
    @@ -46,11 +46,11 @@ Complement versions are also provided, both with explicit and implicit (default) policy.

    -
    using boost::math::policies::policy; // May be needed by users defining their own policies.
-using boost::math::complement; // Will be needed by users who want to use complements.
-
    +
    using boost::math::policies::policy; // May be needed by users defining their own policies.
+using boost::math::complement; // Will be needed by users who want to use complements.
+
    - + find_location function
    @@ -62,25 +62,25 @@ 

    namespace boost{ namespace math{
 
-template <class Dist, class Policy> // explicit error handling policy
-  typename Dist::value_type find_location( // For example, normal mean.
-  typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
-  // For example, a nominal minimum acceptable z, so that p * 100 % are > z
-  typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
-  typename Dist::value_type scale, // scale parameter, for example, normal standard deviation.
-  const Policy& pol);
+template <class Dist, class Policy> // explicit error handling policy
+  typename Dist::value_type find_location( // For example, normal mean.
+  typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
+  // For example, a nominal minimum acceptable z, so that p * 100 % are > z
+  typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
+  typename Dist::value_type scale, // scale parameter, for example, normal standard deviation.
+  const Policy& pol);
 
-template <class Dist>  // with default policy.
-  typename Dist::value_type find_location( // For example, normal mean.
-  typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
-  // For example, a nominal minimum acceptable z, so that p * 100 % are > z
-  typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
-  typename Dist::value_type scale); // scale parameter, for example, normal standard deviation.
-
-  }} // namespaces
-
    +template <class Dist> // with default policy. + typename Dist::value_type find_location( // For example, normal mean. + typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. + // For example, a nominal minimum acceptable z, so that p * 100 % are > z + typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. + typename Dist::value_type scale); // scale parameter, for example, normal standard deviation. + + }} // namespaces +
    - + find_scale function
    @@ -93,21 +93,21 @@ 
    namespace boost{ namespace math{ 
 
 template <class Dist, class Policy>
-  typename Dist::value_type find_scale( // For example, normal mean.
-  typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
-  // For example, a nominal minimum acceptable weight z, so that p * 100 % are > z
-  typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
-  typename Dist::value_type location, // location parameter, for example, normal distribution mean.
-  const Policy& pol);
+  typename Dist::value_type find_scale( // For example, normal mean.
+  typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
+  // For example, a nominal minimum acceptable weight z, so that p * 100 % are > z
+  typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
+  typename Dist::value_type location, // location parameter, for example, normal distribution mean.
+  const Policy& pol);
 
- template <class Dist> // with default policy.
-   typename Dist::value_type find_scale( // For example, normal mean.
-   typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p.
-   // For example, a nominal minimum acceptable z, so that p * 100 % are > z
-   typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z.
-   typename Dist::value_type location) // location parameter, for example, normal distribution mean.
-}} // namespaces
-
    + template <class Dist> // with default policy. + typename Dist::value_type find_scale( // For example, normal mean. + typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. + // For example, a nominal minimum acceptable z, so that p * 100 % are > z + typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. + typename Dist::value_type location) // location parameter, for example, normal distribution mean. +}} // namespaces +

    All argument must be finite, otherwise domain_error is called. @@ -130,9 +130,8 @@

    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html index cdf4982cd..6078a18c6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html @@ -3,7 +3,7 @@ Distributions - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -89,9 +89,8 @@
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index 7cd3d4c49..7e22007e9 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -3,7 +3,7 @@ Bernoulli Distribution - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Bernoulli Distribution @@ -47,13 +47,13 @@ typedef RealType value_type; typedef Policy policy_type; - bernoulli_distribution(RealType p); // Constructor. - // Accessor function. - RealType success_fraction() const - // Probability of success (as a fraction). - }; -}} // namespaces - + bernoulli_distribution(RealType p); // Constructor. + // Accessor function. + RealType success_fraction() const + // Probability of success (as a fraction). + }; +}} // namespaces +

    The Bernoulli distribution is a discrete distribution of the outcome of a single trial with only two results, 0 (failure) or 1 (success), @@ -87,7 +87,7 @@

    - + Member Functions
    @@ -103,7 +103,7 @@ Returns the success_fraction parameter of this distribution.

    - + Non-member Accessors
    @@ -128,7 +128,7 @@ exception and make an error message available.

    - + Accuracy

    @@ -136,7 +136,7 @@ and so should have errors within an epsilon or two.

    - + Implementation

    @@ -327,25 +327,24 @@

    - + References
    -
    -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index be7e501d3..8df05ab9e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -3,7 +3,7 @@ Beta Distribution - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Beta Distribution @@ -39,48 +39,48 @@ class Policy = policies::policy<> > class beta_distribution; -// typedef beta_distribution<double> beta; -// Note that this is deliberately NOT provided, -// to avoid a clash with the function name beta. - +// typedef beta_distribution<double> beta; +// Note that this is deliberately NOT provided, +// to avoid a clash with the function name beta. + template <class RealType, class Policy> class beta_distribution { public: typedef RealType value_type; typedef Policy policy_type; - // Constructor from two shape parameters, alpha & beta: - beta_distribution(RealType a, RealType b); + // Constructor from two shape parameters, alpha & beta: + beta_distribution(RealType a, RealType b); - // Parameter accessors: - RealType alpha() const; + // Parameter accessors: + RealType alpha() const; RealType beta() const; - // Parameter estimators of alpha or beta from mean and variance. - static RealType find_alpha( - RealType mean, // Expected value of mean. - RealType variance); // Expected value of variance. - - static RealType find_beta( - RealType mean, // Expected value of mean. - RealType variance); // Expected value of variance. - - // Parameter estimators from from - // either alpha or beta, and x and probability. - + // Parameter estimators of alpha or beta from mean and variance. static RealType find_alpha( - RealType beta, // from beta. - RealType x, // x. - RealType probability); // cdf - + RealType mean, // Expected value of mean. + RealType variance); // Expected value of variance. + static RealType find_beta( - RealType alpha, // alpha. - RealType x, // probability x. - RealType probability); // probability cdf. -}; + RealType mean, // Expected value of mean. + RealType variance); // Expected value of variance. -}} // namespaces - + // Parameter estimators from from + // either alpha or beta, and x and probability. + + static RealType find_alpha( + RealType beta, // from beta. + RealType x, // x. + RealType probability); // cdf + + static RealType find_beta( + RealType alpha, // alpha. + RealType x, // probability x. + RealType probability); // probability cdf. +}; + +}} // namespaces +

    The class type beta_distribution represents a beta @@ -132,12 +132,12 @@ whose apex is away from the centre (where x = half).

    - + Member Functions
    - + Constructor 
    beta_distribution(RealType alpha, RealType beta);
@@ -164,7 +164,7 @@
             yellow in the graph above).
           
    
 
    
-
+
             Parameter
             Accessors
           
    
@@ -184,11 +184,11 @@
             So for example:
           
    
 
    beta_distribution<> mybeta(2, 5);
-assert(mybeta.alpha() == 2.);  // mybeta.alpha() returns 2
-assert(mybeta.beta() == 5.);   // mybeta.beta()  returns 5
-
    
+assert(mybeta.alpha() == 2.);  // mybeta.alpha() returns 2
+assert(mybeta.beta() == 5.);   // mybeta.beta()  returns 5
+
    - + Parameter Estimators
    @@ -209,39 +209,39 @@ Buster but this is not yet implemented here. 

    static RealType find_alpha(
-  RealType mean, // Expected value of mean.
-  RealType variance); // Expected value of variance.
-
    + RealType mean, // Expected value of mean. + RealType variance); // Expected value of variance. +

    Returns the unique value of α   that corresponds to a beta distribution with mean mean and variance variance. 

    static RealType find_beta(
-  RealType mean, // Expected value of mean.
-  RealType variance); // Expected value of variance.
-
    + RealType mean, // Expected value of mean. + RealType variance); // Expected value of variance. +

    Returns the unique value of β   that corresponds to a beta distribution with mean mean and variance variance. 

    static RealType find_alpha(
-  RealType beta, // from beta.
-  RealType x, //  x.
-  RealType probability); // probability cdf
-
    + RealType beta, // from beta. + RealType x, // x. + RealType probability); // probability cdf +

    Returns the value of α   that gives: cdf(beta_distribution<RealType>(alpha, beta), x) == probability. 

    static RealType find_beta(
-  RealType alpha, // alpha.
-  RealType x, // probability x.
-  RealType probability); // probability cdf.
-
    + RealType alpha, // alpha. + RealType x, // probability x. + RealType probability); // probability cdf. +

    Returns the value of β   that gives: cdf(beta_distribution<RealType>(alpha, beta), x) == probability.

    - + Non-member Accessor Functions
    @@ -263,7 +263,7 @@ Mathworld.

    - + Applications

    @@ -276,7 +276,7 @@ statistical inference.

    - + Related distributions
    @@ -303,7 +303,7 @@ Distribution with its p parameter set to x.

    - + Accuracy

    @@ -315,7 +315,7 @@ please refer to these functions for information on accuracy.

    - + Implementation

    @@ -594,7 +594,7 @@

    - + References

    @@ -612,9 +612,8 @@ -
    Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

    +

    Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index 126139994..0ee344619 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -3,7 +3,7 @@ Binomial Distribution - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Binomial Distribution @@ -51,15 +51,15 @@ static const unspecified-type clopper_pearson_exact_interval; static const unspecified-type jeffreys_prior_interval; - // construct: - binomial_distribution(RealType n, RealType p); + // construct: + binomial_distribution(RealType n, RealType p); - // parameter access:: - RealType success_fraction() const; + // parameter access:: + RealType success_fraction() const; RealType trials() const; - // Bounds on success fraction: - static RealType find_lower_bound_on_p( + // Bounds on success fraction: + static RealType find_lower_bound_on_p( RealType trials, RealType successes, RealType probability, @@ -70,26 +70,26 @@ RealType probability, unspecified-type method = clopper_pearson_exact_interval); - // estimate min/max number of trials: - static RealType find_minimum_number_of_trials( - RealType k, // number of events - RealType p, // success fraction - RealType alpha); // risk level - + // estimate min/max number of trials: + static RealType find_minimum_number_of_trials( + RealType k, // number of events + RealType p, // success fraction + RealType alpha); // risk level + static RealType find_maximum_number_of_trials( - RealType k, // number of events - RealType p, // success fraction - RealType alpha); // risk level -}; + RealType k, // number of events + RealType p, // success fraction + RealType alpha); // risk level +}; -}} // namespaces - +}} // namespaces +

    The class type binomial_distribution represents a binomial distribution: it is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are labelled "success" - and "failure". The binomial distribution + and "failure". The distribution is used to obtain the probability of observing k successes in N trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials. @@ -161,12 +161,12 @@

    - + Member Functions
    - + Construct 
    binomial_distribution(RealType n, RealType p);
@@ -183,7 +183,7 @@
             otherwise calls domain_error.
           
    
 
    
-
+
             Accessors
           
    
 
    RealType success_fraction() const;
@@ -199,7 +199,7 @@
             was constructed.
           
    
 
    
-
+
             Lower
             Bound on the Success Fraction
           
    
@@ -305,7 +305,7 @@
             limits illustrated in the case of the binomial. Biometrika 26 404-413.
           
    
 
    
-
+
             Upper
             Bound on the Success Fraction
           
    
@@ -383,15 +383,15 @@
    - + Estimating the Number of Trials Required for a Certain Number of Successes 
    static RealType find_minimum_number_of_trials(
-   RealType k,     // number of events
-   RealType p,     // success fraction
-   RealType alpha); // probability threshold
-
    + RealType k, // number of events + RealType p, // success fraction + RealType alpha); // probability threshold +

    This function estimates the minimum number of trials required to ensure that more than k events is observed with a level of risk alpha @@ -425,16 +425,16 @@ of seeing 10 events that occur with frequency one half.

    - + Estimating the Maximum Number of Trials to Ensure no more than a Certain Number of Successes 
    static RealType find_maximum_number_of_trials(
-   RealType k,     // number of events
-   RealType p,     // success fraction
-   RealType alpha); // probability threshold
-
    + RealType k, // number of events + RealType p, // success fraction + RealType alpha); // probability threshold +

    This function estimates the maximum number of trials we can conduct to ensure that k successes or fewer are observed, with a risk alpha @@ -473,7 +473,7 @@ Worked Example.

    - + Non-member Accessors
    @@ -622,7 +622,7 @@

    - + Examples

    @@ -630,7 +630,7 @@ examples are available illustrating the use of the binomial distribution.

    - + Accuracy

    @@ -640,7 +640,7 @@ please refer to these functions for information on accuracy.

    - + Implementation

    @@ -884,20 +884,20 @@

    - + References
    -
      -
    • +
      -
      Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

      +

      Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index e4990a1f0..3f7976ec3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -3,7 +3,7 @@ Cauchy-Lorentz Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Cauchy-Lorentz Distribution @@ -88,7 +88,7 @@

      - + Member Functions
      @@ -114,7 +114,7 @@ Returns the scale parameter of the distribution.

      - + Non-member Accessors
      @@ -148,7 +148,7 @@ The domain of the random variable is [-[max_value], +[min_value]].

      - + Accuracy

      @@ -157,7 +157,7 @@ have very low error rates.

      - + Implementation

      @@ -273,19 +273,19 @@

    - + References
    -
      -
    • +
      -
      Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

      +

      Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index c8a221fe1..fa7e5e384 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -3,7 +3,7 @@ Chi Squared Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Chi Squared Distribution @@ -48,14 +48,14 @@ typedef RealType value_type; typedef Policy policy_type; - // Constructor: - chi_squared_distribution(RealType i); + // Constructor: + chi_squared_distribution(RealType i); - // Accessor to parameter: - RealType degrees_of_freedom()const; + // Accessor to parameter: + RealType degrees_of_freedom()const; - // Parameter estimation: - static RealType find_degrees_of_freedom( + // Parameter estimation: + static RealType find_degrees_of_freedom( RealType difference_from_mean, RealType alpha, RealType beta, @@ -63,8 +63,8 @@ RealType hint = 100); }; -}} // namespaces - +}} // namespaces +

      The Chi-Squared distribution is one of the most widely used distributions in statistical tests. If χi   are ν   @@ -87,7 +87,7 @@ independent, normally distributed random

      - + Member Functions
      @@ -170,7 +170,7 @@ independent, normally distributed random NIST Engineering Statistics Handbook, Section 7.2.3.2.

      - + Non-member Accessors
      @@ -196,7 +196,7 @@ independent, normally distributed random The domain of the random variable is [0, +∞].

      - + Examples

      @@ -204,7 +204,7 @@ independent, normally distributed random are available illustrating the use of the Chi Squared Distribution.

      - + Accuracy

      @@ -212,7 +212,7 @@ independent, normally distributed random gamma functions: please refer to the accuracy data for those functions.

      - + Implementation

      @@ -379,19 +379,19 @@ independent, normally distributed random

    - + References
    -
      -
    • +
      -
      Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, - Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and - Thijs van den Berg

      +

      Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno + Lalande, Johan Råde, Gautam Sewani and 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)

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index 4b4f17712..460dd285f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -3,7 +3,7 @@ Exponential Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Exponential Distribution @@ -71,7 +71,7 @@

      - + Member Functions
      @@ -91,7 +91,7 @@ Accessor function returns the lambda parameter of the distribution.

      - + Non-member Accessors
      @@ -111,7 +111,7 @@ The domain of the random variable is [0, +∞].

      - + Accuracy

      @@ -122,7 +122,7 @@ should have very low error rates.

      - + Implementation

      @@ -283,24 +283,24 @@

    - + references
    -