[DEV] add v1.76.0

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2021-10-05 21:37:46 +02:00
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Complements are supported too - and when to use them</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="generic.html" title="Generic operations common to all distributions are non-member functions">
<link rel="next" href="parameters.html" title="Parameters can be calculated">
</head>
@@ -183,11 +183,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Generic operations common to all distributions are non-member functions</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="objects.html" title="Distributions are Objects">
<link rel="next" href="complements.html" title="Complements are supported too - and when to use them">
</head>
@@ -108,11 +108,14 @@
and Wolfram MathWorld) by placing a semi-colon or vertical bar) <span class="emphasis"><em>after</em></span>
the <a href="http://en.wikipedia.org/wiki/Random_variable" target="_top">random
variable</a> (whose value you 'choose'), to separate the variate
from the parameter(s) that defines the shape of the distribution.<br>
from the parameter(s) that defines the shape of the distribution.
</p>
<p>
For example, the binomial distribution probability distribution function
(PDF) is written as <span class="emphasis"><em>f(k| n, p)</em></span> = Pr(K = k|n, p)
= probability of observing k successes out of n trials. K is the <a href="http://en.wikipedia.org/wiki/Random_variable" target="_top">random variable</a>,
k is the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
(PDF) is written as <span class="serif_italic"><span class="emphasis"><em>f(k| n, p)</em></span>
= Pr(K = k|n, p) = </span> probability of observing k successes out
of n trials. K is the <a href="http://en.wikipedia.org/wiki/Random_variable" target="_top">random
variable</a>, k is the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
variate</a>, the parameters are n (trials) and p (probability).
</p>
</td></tr>
@@ -210,19 +213,19 @@
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 <span class="emphasis"><em>outwards</em></span>:
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 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.
that is to say, lower quantiles - where the probability is less than
0.5 are rounded down, while upper quantiles - where the probability is
greater than 0.5 - are rounded up. 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, or return a real-valued result using <a class="link" href="../../pol_overview.html" title="Policy Overview">Policies</a>.
It is strongly recommended that you read the tutorial <a class="link" href="../../pol_tutorial/understand_dis_quant.html" title="Understanding Quantiles of Discrete Distributions">Understanding
Quantiles of Discrete Distributions</a> before using the quantile
function on a discrete distribtion. The <a class="link" href="../../pol_ref/discrete_quant_ref.html" title="Discrete Quantile Policies">reference
function on a discrete distribution. The <a class="link" href="../../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>
@@ -237,11 +240,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Headers and Namespaces</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="prev" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="next" href="objects.html" title="Distributions are Objects">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -28,16 +28,17 @@
Namespaces</a>
</h4></div></div></div>
<p>
All the code in this library is inside namespace boost::math.
All the code in this library is inside <code class="computeroutput"><span class="keyword">namespace</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code>.
</p>
<p>
In order to use a distribution <span class="emphasis"><em>my_distribution</em></span> you
will need to include either the header &lt;boost/math/my_distribution.hpp&gt;
or the "include all the distributions" header: &lt;boost/math/distributions.hpp&gt;.
will need to include either the header(s) <code class="computeroutput"><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">my_distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
(quicker compiles), or the "include all the distributions" header:
<code class="computeroutput"><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">hpp</span><span class="special">&gt;</span></code>.
</p>
<p>
For example, to use the Students-t distribution include either &lt;boost/math/students_t.hpp&gt;
or &lt;boost/math/distributions.hpp&gt;
For example, to use the Students-t distribution include either <code class="computeroutput"><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">students_t</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> or <code class="computeroutput"><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">hpp</span><span class="special">&gt;</span></code>
</p>
<p>
You also need to bring distribution names into scope, perhaps with a <code class="computeroutput"><span class="keyword">using</span> <span class="keyword">namespace</span>
@@ -54,18 +55,18 @@
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top"><p>
Some math function names are also used in namespace std so including
&lt;random&gt; could cause ambiguity!
Some math function names are also used in <code class="computeroutput"><span class="keyword">namespace</span>
<span class="identifier">std</span></code> so including <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">random</span><span class="special">&gt;</span></code> could cause ambiguity!
</p></td></tr>
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Distributions are Objects</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="headers.html" title="Headers and Namespaces">
<link rel="next" href="generic.html" title="Generic operations common to all distributions are non-member functions">
</head>
@@ -28,13 +28,8 @@
are Objects</a>
</h4></div></div></div>
<p>
Each kind of distribution in this library is a class type - an object.
</p>
<p>
<a class="link" href="../../../policy.html" title="Chapter&#160;18.&#160;Policies: Controlling Precision, Error Handling etc">Policies</a> 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.
Each kind of distribution in this library is a class type - an object,
with member functions.
</p>
<div class="tip"><table border="0" summary="Tip">
<tr>
@@ -47,6 +42,12 @@
comparison to other statistics libraries.</a>
</p></td></tr>
</table></div>
<p>
<a class="link" href="../../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a> provide optional 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 distributions
behave.
</p>
<p>
Making distributions class types does two things:
</p>
@@ -117,11 +118,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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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@@ -1,11 +1,11 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Parameters can be calculated</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="complements.html" title="Complements are supported too - and when to use them">
<link rel="next" href="summary.html" title="Summary">
</head>
@@ -56,11 +56,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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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@@ -1,11 +1,11 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Summary</title>
<link rel="stylesheet" href="../../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Overview of Distributions">
<link rel="home" href="../../../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Overview of Statistical Distributions">
<link rel="prev" href="parameters.html" title="Parameters can be calculated">
<link rel="next" href="../weg.html" title="Worked Examples">
</head>
@@ -58,11 +58,11 @@
</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 &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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>