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+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Lists and Tables</title>
+<link rel="stylesheet" href="../../../../doc/html/boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_8125">
+<link rel="home" href="../index.html" title="Document To Test Formatting">
+<link rel="up" href="../index.html" title="Document To Test Formatting">
+<link rel="prev" href="blurbs.html" title="Blurbs">
+<link rel="next" href="images.html" title="Images">
+</head>
+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
+<table cellpadding="2" width="100%"><tr>
+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td>
+<td align="center"><a href="../../../../index.html">Home</a></td>
+<td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td>
+<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
+<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
+<td align="center"><a href="../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="blurbs.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="images.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="document_to_test_formatting.lists_and_tables"></a><a class="link" href="lists_and_tables.html" title="Lists and Tables">Lists and
+ Tables</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists">Lists</a></span></dt>
+<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists">Variable
+ Lists</a></span></dt>
+<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables">Tables</a></span></dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="document_to_test_formatting.lists_and_tables.lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists" title="Lists">Lists</a>
+</h3></div></div></div>
+<p>
+ A numbered list:
+ </p>
+<div class="orderedlist"><ol type="1">
+<li>
+ One
+ </li>
+<li>
+ Two
+ </li>
+<li>
+ Three
+ <div class="orderedlist"><ol type="a">
+<li>
+ Three.a
+ </li>
+<li>
+ Three.b
+ </li>
+<li>
+ Three.c
+ </li>
+</ol></div>
+</li>
+<li>
+ Four
+ <div class="orderedlist"><ol type="a"><li>
+ Four.a
+ <div class="orderedlist"><ol type="i">
+<li>
+ Four.a.i
+ </li>
+<li>
+ Four.a.ii
+ </li>
+</ol></div>
+</li></ol></div>
+</li>
+<li>
+ Five
+ </li>
+</ol></div>
+<p>
+ An unordered list:
+ </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+ First
+ </li>
+<li>
+ Second
+ </li>
+<li>
+ Third
+ </li>
+</ul></div>
+<p>
+ A mixture of the two:
+ </p>
+<div class="orderedlist"><ol type="1">
+<li>
+ 1
+ <div class="itemizedlist"><ul type="disc">
+<li>
+ 1.a
+ <div class="orderedlist"><ol type="a">
+<li>
+ 1.a.1
+ </li>
+<li>
+ 1.a.2
+ </li>
+</ol></div>
+</li>
+<li>
+ 1.b
+ </li>
+</ul></div>
+</li>
+<li>
+ 2
+ <div class="itemizedlist"><ul type="disc">
+<li>
+ 2.a
+ </li>
+<li>
+ 2.b
+ <div class="orderedlist"><ol type="a">
+<li>
+ 2.b.1
+ </li>
+<li>
+ 2.b.2
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ 2.b.2.a
+ </li>
+<li>
+ 2.b.2.b
+ </li>
+</ul></div>
+</li>
+</ol></div>
+</li>
+</ul></div>
+</li>
+</ol></div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="document_to_test_formatting.lists_and_tables.variable_lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists" title="Variable Lists">Variable
+ Lists</a>
+</h3></div></div></div>
+<div class="variablelist">
+<p class="title"><b>A Variable List</b></p>
+<dl>
+<dt><span class="term">term 1</span></dt>
+<dd><p>
+ The definition of term 1
+ </p></dd>
+<dt><span class="term">term 2</span></dt>
+<dd><p>
+ The definition of term 2
+ </p></dd>
+<dt><span class="term">term 3</span></dt>
+<dd><p>
+ The definition of term 3
+ </p></dd>
+</dl>
+</div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="document_to_test_formatting.lists_and_tables.tables"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables" title="Tables">Tables</a>
+</h3></div></div></div>
+<p>
+ Here's a big table with code and other tricky things:
+ </p>
+<div class="table">
+<a name="id537940"></a><p class="title"><b>Table 1. Notes on the Implementation of the Beta Distribution</b></p>
+<div class="table-contents"><table class="table" summary="Notes on the Implementation of the Beta Distribution">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ <p>
+ Function
+ </p>
+ </th>
+<th>
+ <p>
+ Implementation Notes
+ </p>
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ <p>
+ pdf
+ </p>
+ </td>
+<td>
+ <p>
+ f(x;&#945;,&#946;) = x<sup>&#945; - 1</sup> (1 - x)<sup>&#946; -1</sup> / B(&#945;, &#946;)
+ </p>
+ <p>
+ Implemented using ibeta_derivative(a, b, x).
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ cdf
+ </p>
+ </td>
+<td>
+ <p>
+ Using the incomplete beta function ibeta(a, b, x)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ cdf complement
+ </p>
+ </td>
+<td>
+ <p>
+ ibetac(a, b, x)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ quantile
+ </p>
+ </td>
+<td>
+ <p>
+ Using the inverse incomplete beta function ibeta_inv(a, b, p)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ quantile from the complement
+ </p>
+ </td>
+<td>
+ <p>
+ ibetac_inv(a, b, q)
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ mean
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ variance
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span>
+ <span class="identifier">b</span> <span class="special">/</span>
+ <span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ mode
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span>
+ <span class="special">/</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="identifier">b</span> <span class="special">+</span> <span class="number">2</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ skewness
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span> <span class="special">*</span>
+ <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ kurtosis excess
+ </p>
+ </td>
+<td>
+ <p>
+ <span class="inlinemediaobject"><img src="../images/beta_dist_kurtosis.png" alt="beta_dist_kurtosis"></span>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ kurtosis
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span>
+ <span class="number">3</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ parameter estimation
+ </p>
+ </td>
+<td>
+ <p>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ alpha
+ </p>
+ <p>
+ from mean and variance
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span>
+ <span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span>
+ <span class="special">(</span><span class="number">1</span>
+ <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">variance</span><span class="special">)-</span>
+ <span class="number">1</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ beta
+ </p>
+ <p>
+ from mean and variance
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="special">(</span><span class="number">1</span>
+ <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span> <span class="special">(((</span><span class="identifier">mean</span>
+ <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span>
+ <span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ The member functions <code class="computeroutput"><span class="identifier">estimate_alpha</span></code>
+ and <code class="computeroutput"><span class="identifier">estimate_beta</span></code>
+ </p>
+ <p>
+ from cdf and probability x
+ </p>
+ <p>
+ and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code>
+ or <code class="computeroutput"><span class="identifier">beta</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ Implemented in terms of the inverse incomplete beta functions
+ </p>
+ <p>
+ ibeta_inva, and ibeta_invb respectively.
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">estimate_alpha</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+<tr>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">estimate_beta</span></code>
+ </p>
+ </td>
+<td>
+ <p>
+ <code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span>
+ <span class="identifier">x</span><span class="special">,</span>
+ <span class="identifier">probability</span><span class="special">)</span></code>
+ </p>
+ </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+<br class="table-break">
+</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 © 2007 John Maddock, Joel de Guzman, Eric Niebler and Matias
+ Capeletto<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
+ </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="blurbs.html"><img src="../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="images.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>