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Boost-Commit : |
From: john_at_[hidden]
Date: 2008-02-06 07:46:53
Author: johnmaddock
Date: 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
New Revision: 43124
URL: http://svn.boost.org/trac/boost/changeset/43124
Log:
Added non-central F docs, plus updated nc beta docs.
Added:
sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_f.qbk (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.svg (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref2.mml (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref2.png (contents, props changed)
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref2.svg (contents, props changed)
Text files modified:
sandbox/math_toolkit/libs/math/doc/sf_and_dist/dist_reference.qbk | 1 +
sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_beta.qbk | 4 ++--
sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/generate.sh | 3 ++-
3 files changed, 5 insertions(+), 3 deletions(-)
Modified: sandbox/math_toolkit/libs/math/doc/sf_and_dist/dist_reference.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/sf_and_dist/dist_reference.qbk (original)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/dist_reference.qbk 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -17,6 +17,7 @@
[include distributions/negative_binomial.qbk]
[include distributions/nc_beta.qbk]
[include distributions/nc_chi_squared.qbk]
+[include distributions/nc_f.qbk]
[include distributions/normal.qbk]
[include distributions/pareto.qbk]
[include distributions/poisson.qbk]
Modified: sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_beta.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_beta.qbk (original)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_beta.qbk 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -80,10 +80,10 @@
Most of the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
are supported: __cdf, __pdf, __quantile,
-__hazard, __chf, __range and __support.
+__median, __mode, __hazard, __chf, __range and __support.
However, the following are not currently implemented:
-__mean, __median, __mode, __variance, __sd, __skewness,
+__mean, __variance, __sd, __skewness,
__kurtosis and __kurtosis_excess.
The domain of the random variable is \[0, 1\].
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_f.qbk
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/distributions/nc_f.qbk 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -0,0 +1,188 @@
+[section:nc_f_dist Non Central F Distribution]
+
+``#include <boost/math/distributions/non_central_f.hpp>``
+
+ namespace boost{ namespace math{
+
+ template <class RealType = double,
+ class ``__Policy`` = ``__policy_class`` >
+ class non_central_f_distribution;
+
+ typedef non_central_f_distribution<> non_central_f;
+
+ template <class RealType, class ``__Policy``>
+ class non_central_f_distribution
+ {
+ public:
+ typedef RealType value_type;
+ typedef Policy policy_type;
+
+ // Constructor:
+ non_central_f_distribution(RealType v1, RealType v2, RealType lambda);
+
+ // Accessor to parameters:
+ RealType degrees_of_freedom1()const;
+ RealType degrees_of_freedom2()const;
+
+ // Accessor to non centrality parameter:
+ RealType non_centrality()const;
+ };
+
+ }} // namespaces
+
+The non-central F distribution is a generalization of the
+[link math_toolkit.dist.dist_ref.dists.f_dist Fisher F distribution].
+It is defined as the ratio
+
+ F = (X/v1) / (Y/v2)
+
+where X is a non-central [chi][super 2]
+random variable with /v1/ degrees of freedom and non centrality parameter [lambda],
+and Y is a central [chi][super 2] random variable with /v2/ degrees of freedom.
+
+This gives the following PDF:
+
+[equation nc_f_ref1]
+
+where L[sub a][super b](c) is a generalised Laguerre polynomial and B(a,b) is the
+beta function, or
+
+[equation nc_f_ref2]
+
+The following graph illustrates how the distribution changes
+for different values of [lambda]:
+
+[$../graphs/nc_f_pdf.png]
+
+[h4 Member Functions]
+
+ non_central_f_distribution(RealType v1, RealType v2, RealType lambda);
+
+Constructs a non-central beta distribution with parameters /v1/ and /v2/
+and non-centrality parameter /lambda/.
+
+Requires v1 > 0, v2 > 0 and lambda >= 0, otherwise calls __domain_error.
+
+ RealType degrees_of_freedom1()const;
+
+Returns the parameter /v1/ from which this object was constructed.
+
+ RealType degrees_of_freedom2()const;
+
+Returns the parameter /v2/ from which this object was constructed.
+
+ RealType non_centrality()const;
+
+Returns the parameter /lambda/ from which this object was constructed.
+
+[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 \[0, +[infin]\].
+
+[h4 Accuracy]
+
+This distribution is implemented in terms of the
+[link math_toolkit.dist.dist_ref.dists.nc_beta_dist non-central beta distribution]:
+refer to that distribution for accuracy data.
+
+[h4 Tests]
+
+Since this distribution is implemented by adapting another distribution,
+the tests consist of basic sanity checks computed by the R statistical
+package and the pbeta and dbeta functions.
+
+[h4 Implementation]
+
+In the following table /v1/ and /v2/ are the first and second
+degrees of freedom parameters of the distribution, [lambda]
+is the non-centrality parameter,
+/x/ is the random variate, /p/ is the probability, and /q = 1-p/.
+
+[table
+[[Function][Implementation Notes]]
+[[pdf][Implemented in terms of the non-central beta PDF using the relation:
+
+f(x;v1,v2;[lambda]) = (v1\/v2) / ((1+y)*(1+y)) * g(y\/(1+y);v1\/2,v2\/2;[lambda])
+
+where g(x; a, b; [lambda]) is the non central beta PDF, and:
+
+y = x * v1 \/ v2
+]]
+[[cdf][Using the relation:
+
+p = B[sub y](v1\/2, v2\/2; [lambda])
+
+where B[sub x](a, b; [lambda]) is the non-central beta distribution CDF and
+
+y = x * v1 \/ v2
+
+]]
+
+[[cdf complement][Using the relation:
+
+q = 1 - B[sub y](v1\/2, v2\/2; [lambda])
+
+where 1 - B[sub x](a, b; [lambda]) is the complement of the
+non-central beta distribution CDF and
+
+y = x * v1 \/ v2
+
+]]
+[[quantile][Using the relation:
+
+x = (bx \/ (1-bx)) * (v1 \/ v2)
+
+where
+
+bx = Q[sub p][super -1](v1\/2, v2\/2; [lambda])
+
+and
+
+Q[sub p][super -1](v1\/2, v2\/2; [lambda])
+
+is the non-central beta quantile.
+
+]]
+[[quantile
+
+from the complement][
+Using the relation:
+
+x = (bx \/ (1-bx)) * (v1 \/ v2)
+
+where
+
+bx = QC[sub q][super -1](v1\/2, v2\/2; [lambda])
+
+and
+
+QC[sub q][super -1](v1\/2, v2\/2; [lambda])
+
+is the non-central beta quantile from the complement.]]
+[[mean][v2 * (v1 + l) \/ (v1 * (v2 - 2))]]
+[[mode][By numeric maximalisation of the PDF.]]
+[[variance][Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html
+ Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.] ]]
+[[skewness][Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html
+ Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.],
+ and to the [@http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html
+ Mathematica documentation] ]]
+[[kurtosis and kurtosis excess]
+ [Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html
+ Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.],
+ and to the [@http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html
+ Mathematica documentation] ]]
+]
+
+[endsect][/section:nc_beta_dist]
+
+[/ nc_beta.qbk
+ 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).
+]
+
Modified: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/generate.sh
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/generate.sh (original)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/generate.sh 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -14,7 +14,7 @@
pngfile=$(basename $svgfile .svg).png
tempfile=temp.mml
# strip html wrappers put in by MathCast:
- cat $svgfile | tr -d "\r\n" | sed -e 's/.*\(<math[^>]*>.*<\/math>\).*/\1/' > $tempfile
+ cat $mmlfile | tr -d "\r\n" | sed -e 's/.*\(<math[^>]*>.*<\/math>\).*/\1/' > $tempfile
echo Generating $svgfile
$python $math2svg $tempfile > $svgfile
@@ -24,3 +24,4 @@
done
+
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.mml 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -0,0 +1,314 @@
+<?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>nc_f_ref1</title>
+<!-- MathML created with MathCast Equation Editor version 0.88 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>f</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mo>,</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>;</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ <mo>+</mo>
+ <mfrac>
+ <mfenced>
+ <mrow>
+ <mi>λ</mi>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mfenced>
+ <mrow>
+ <mn>2</mn>
+ <mfenced>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>+</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfenced>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mi>x</mi>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>+</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mfenced>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mo>+</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mfenced>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <mfrac>
+ <mrow>
+ <mi>Γ</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ </mfenced>
+ <mi>Γ</mi>
+ <mfenced>
+ <mrow>
+ <mn>1</mn>
+ <mo>+</mo>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mfenced>
+ <msubsup>
+ <mi>L</mi>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msubsup>
+ <mfenced>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mrow>
+ <mi>λ</mi>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mi>x</mi>
+ </mrow>
+ <mrow>
+ <mn>2</mn>
+ <mfenced>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>+</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mi>x</mi>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ </mrow>
+ <mrow>
+ <mi>B</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mo>,</mo>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mrow>
+ </mfenced>
+ <mi>Γ</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mn>1</mn>
+ <mn>2</mn>
+ </mfrac>
+ <mfenced>
+ <mrow>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mo>+</mo>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfenced>
+ </mrow>
+ </mfrac>
+ </mrow>
+</math>
+</body>
+</html>
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.png
==============================================================================
Binary file. No diff available.
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref1.svg
==============================================================================
Binary file. No diff available.
Added: sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref2.mml
==============================================================================
--- (empty file)
+++ sandbox/math_toolkit/libs/math/doc/sf_and_dist/equations/nc_f_ref2.mml 2008-02-06 07:46:52 EST (Wed, 06 Feb 2008)
@@ -0,0 +1,202 @@
+<?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>nc_f_ref2</title>
+<!-- MathML created with MathCast Equation Editor version 0.88 -->
+</head>
+<body>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
+ <mrow>
+ <mi>f</mi>
+ <mfenced>
+ <mrow>
+ <mi>x</mi>
+ <mo>;</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ <mo>,</mo>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ <mo>;</mo>
+ <mi>λ</mi>
+ </mrow>
+ </mfenced>
+ <mspace width="1em"/>
+ <mo>=</mo>
+ <mspace width="1em"/>
+ <munderover>
+ <mo>∑</mo>
+ <mrow>
+ <mi>k</mi>
+ <mo>=</mo>
+ <mn>0</mn>
+ </mrow>
+ <mi>∞</mi>
+ </munderover>
+ <mfrac>
+ <mrow>
+ <msup>
+ <mi>e</mi>
+ <mrow>
+ <mo>−</mo>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mi>λ</mi>
+ <mn>2</mn>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mi>k</mi>
+ </msup>
+ </mrow>
+ <mrow>
+ <mi>B</mi>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mn>2,</mn>
+ </mfrac>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>k</mi>
+ </mrow>
+ </mfenced>
+ <mi>k</mi>
+ <mo>!</mo>
+ </mrow>
+ </mfrac>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>k</mi>
+ </mrow>
+ </msup>
+ <msup>
+ <mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mrow>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ <mo>+</mo>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mi>x</mi>
+ </mrow>
+ </mfrac>
+ </mrow>
+ </mfenced>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mo>+</mo>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>2</mn>
+ </msub>
+ </mrow>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>k</mi>
+ </mrow>
+ </msup>
+ <msup>
+ <mi>x</mi>
+ <mrow>
+ <mfrac>
+ <mrow>
+ <msub>
+ <mi>ν</mi>
+ <mn>1</mn>
+ </msub>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
+ <mo>+</mo>
+ <mi>k</mi>
+ <mo>−</mo>
+ <mn>1</mn>
+ </mrow>
+ </msup>
+ </mrow>
+</math>
+</body>
+</html>
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