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)
@@ -513,7 +513,7 @@Last revised: October 13, 2011 at 15:53:36 GMT |
+Last revised: December 21, 2011 at 17:52:13 GMT |
A B C D E F G H I K L M N P Q R S T U V W Z
B C D E F G H I L M N P R S T U W
A B C D E F G H I L N O P R S T U V W
A B C D E F G H I K L M N O P Q R S T U V W Z
@@ -84,9 +84,9 @@
These could still provide sufficient accuracy for some speed-critical applications.
-@@ -129,9 +129,9 @@ a power of two (in order to ensure that the result is an exactly representable binary value).
-@@ -155,9 +155,9 @@ fail on other systems where long double is more accurate than double. Check first that the suffix L is present, and then that the tolerance is big enough.
-@@ -223,9 +223,9 @@ done for most examples.
@@ -257,9 +257,9 @@ domain error occurs. Catching exceptions is therefore strongly recommended.
-@@ -292,9 +292,9 @@ Mathematica Basic Statistics. give more detail, in particular for discrete distributions.
-@@ -336,9 +336,9 @@ What happens at (and near), poles can be controlled through error handling policies.
-@@ -363,9 +363,9 @@ for too many distributions to be generally applicable. Because they are non-member functions, they can be added if required.
-@@ -418,9 +418,9 @@ still need to be accurately calculated, even if they can be in error compared to the "true" minimax solution.
-@@ -479,9 +479,9 @@
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-
@@ -504,9 +504,9 @@ next C++ std revision, so hopefully all compilers will be required to do the right thing here at some point.
-@@ -545,9 +545,9 @@ unfortunately it appears to suffer from very poor accuracy in areas where the underlying special function is known to be difficult to implement.
-@@ -730,9 +730,9 @@ done MathML is not currently present in the Docbook output, or in the generated HTML: this needs further investigation.
-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 8dd7ffeba..fc595d467 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -26,9 +26,9 @@
-Why base gamma and gamma-like functions on the Lanczos approximation? @@ -98,10 +98,9 @@ use similar analytic combinations of power terms, to combine gamma and beta functions divided by large powers into single (simpler) expressions.
-The Lanczos Approximation to the Gamma Function is given by: @@ -160,9 +159,9 @@ so take care when referring to the literature in this field.
-@@ -204,9 +203,9 @@ on N, this product should be computed first, and then multiplied by F as the last step.
-@@ -534,9 +533,9 @@ an inexact value: this reduces accuracy in the common case that the input is exact, and so isn't used for the gamma function.
-@@ -97,9 +97,9 @@ 03-0097, A Proposal to Add Mathematical Special Functions to the C++ Standard Library (version 2), Walter E. Brown
-We found (and used to create cross-check spot values - as far as their accuracy @@ -119,9 +119,10 @@ http://www.adsciengineering.com/bpdcalc/ Binomial Probability Distribution Calculator.
-Cephes library by Shephen 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 8be2aa9dc..62b50104f 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 @@ -77,9 +77,9 @@ errors differ by a factor of 2, can actually be accurate to the same number of binary digits. You have been warned!
-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 041a476cf..17c6e67ab 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -93,10 +93,10 @@ Unfortunately we don't know where the extrema of the error function are located!
-The Remez method is an iterative technique which, given a broad range of @@ -173,10 +173,10 @@
The first step in the Remez method, given our current set of N+2 Chebyshev @@ -204,10 +204,10 @@ not located at the extrema, but the maximum relative error has now dropped to 5.6x10-4.
-The second step is to locate the extrema of the new approximation, which @@ -233,9 +233,9 @@
In our example we perform multi-point exchange.
-The Remez method then performs steps 1 and 2 above iteratively until the @@ -249,9 +249,9 @@
@@ -298,9 +298,9 @@ error drops to 8.7x10-5. That's a 5 fold increase in accuracy, for the same number of terms overall.
-@@ -406,10 +406,10 @@ It's clearly still not ideal, but it is only a few percent away from our desired minimax solution (5x10-4).
-The following lists some of the things to check if the Remez method goes @@ -460,9 +460,9 @@ over, say [0, b], for some smallish value b. -
The original references for the Remez Method and it's extension to rational 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 a2e2ab52b..088c7d0eb 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 @@ -27,9 +27,9 @@ Distribution Algorithms -
@@ -49,13 +49,12 @@
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.-
-
#include <boost/math/distributions/find_location.hpp>
@@ -79,18 +78,17 @@ }} // namespaces -
-
#include <boost/math/distributions/find_scale.hpp>
-
namespace boost{ namespace math{ +namespace boost{ namespace math{ template <class Dist, class Policy> typename Dist::value_type find_scale( // For example, normal mean. 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 7e22007e9..0c16c60a3 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 @@ -28,16 +28,15 @@ Distribution
-
#include <boost/math/distributions/bernoulli.hpp>
namespace boost{ namespace math{ - template <class RealType = double, + template <class RealType = double, class Policy = policies::policy<> > class bernoulli_distribution; - + typedef bernoulli_distribution<> bernoulli; template <class RealType, class Policy> @@ -51,7 +50,7 @@ // Accessor function. RealType success_fraction() const // Probability of success (as a fraction). - }; + }; }} // namespaces
@@ -86,9 +85,9 @@
bernoulli_distribution(RealType p); @@ -102,9 +101,9 @@Returns the success_fraction parameter of this distribution.
-- - Non-member +
+ + Non-member Accessors
@@ -127,17 +126,17 @@ Outside this range, functions are undefined, or may throw domain_error exception and make an error message available.
-- - Accuracy +
+ + Accuracy
The Bernoulli distribution is implemented with simple arithmetic operators and so should have errors within an epsilon or two.
-- - Implementation +
+ + Implementation
In the following table p is the probability of success @@ -326,9 +325,9 @@ -
- - References +
+ + References
- 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 8df05ab9e..a1e0267c8 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 @@ -28,14 +28,13 @@ Distribution
-
#include <boost/math/distributions/beta.hpp>-
namespace boost{ namespace math{ +namespace boost{ namespace math{ - template <class RealType = double, + template <class RealType = double, class Policy = policies::policy<> > class beta_distribution; @@ -51,28 +50,28 @@ typedef Policy policy_type; // Constructor from two shape parameters, alpha & beta: beta_distribution(RealType a, RealType b); - + // 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. - + 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. @@ -131,14 +130,14 @@ β, then the shape is asymmetric and could be approximated by a triangle whose apex is away from the centre (where x = half). -- - Member +
+ + Member Functions
-- - Constructor +
+ + Constructor
beta_distribution(RealType alpha, RealType beta);@@ -163,9 +162,9 @@ Constructs a the beta distribution with alpha=2 and beta=5 (shown in yellow in the graph above). -- - Parameter +
+ + Parameter Accessors
RealType alpha() const; @@ -187,9 +186,9 @@ assert(mybeta.alpha() == 2.); // mybeta.alpha() returns 2 assert(mybeta.beta() == 5.); // mybeta.beta() returns 5-- - Parameter +
+ + Parameter Estimators
@@ -240,9 +239,9 @@
Returns the value of β that gives:
-cdf(beta_distribution<RealType>(alpha, beta), x) == probability.- - Non-member +
+ + Non-member Accessor Functions
@@ -262,9 +261,9 @@ at Wolfram Mathworld.
-- - Applications +
+ + Applications
The beta distribution can be used to model events constrained to take @@ -275,9 +274,9 @@ It is also widely used in Bayesian statistical inference.
-- - Related +
+ + Related distributions
@@ -302,9 +301,9 @@ are less than x, a probability given by summing over the Binomial Distribution with its p parameter set to x.
-- - Accuracy +
+ + Accuracy
This distribution is implemented using the beta @@ -314,9 +313,9 @@ and ibetac; please refer to these functions for information on accuracy.
-- - Implementation +
+ + Implementation
In the following table a and b @@ -593,9 +592,9 @@ -
- - References +
+ + References
-
#include <boost/math/distributions/binomial.hpp>
-
