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- <html>
- <head>
- <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
- <title>Lists and Tables</title>
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- <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>
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- <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
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- </div>
- <div class="section">
- <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">
- <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 class="orderedlist" type="1">
- <li class="listitem">
- One
- </li>
- <li class="listitem">
- Two
- </li>
- <li class="listitem">
- Three
- <div class="orderedlist"><ol class="orderedlist" type="a">
- <li class="listitem">
- Three.a
- </li>
- <li class="listitem">
- Three.b
- </li>
- <li class="listitem">
- Three.c
- </li>
- </ol></div>
- </li>
- <li class="listitem">
- Four
- <div class="orderedlist"><ol class="orderedlist" type="a"><li class="listitem">
- Four.a
- <div class="orderedlist"><ol class="orderedlist" type="i">
- <li class="listitem">
- Four.a.i
- </li>
- <li class="listitem">
- Four.a.ii
- </li>
- </ol></div>
- </li></ol></div>
- </li>
- <li class="listitem">
- Five
- </li>
- </ol></div>
- <p>
- An unordered list:
- </p>
- <div class="itemizedlist"><ul class="itemizedlist" type="disc">
- <li class="listitem">
- First
- </li>
- <li class="listitem">
- Second
- </li>
- <li class="listitem">
- Third
- </li>
- </ul></div>
- <p>
- A mixture of the two:
- </p>
- <div class="orderedlist"><ol class="orderedlist" type="1">
- <li class="listitem">
- 1
- <div class="itemizedlist"><ul class="itemizedlist" type="disc">
- <li class="listitem">
- 1.a
- <div class="orderedlist"><ol class="orderedlist" type="a">
- <li class="listitem">
- 1.a.1
- </li>
- <li class="listitem">
- 1.a.2
- </li>
- </ol></div>
- </li>
- <li class="listitem">
- 1.b
- </li>
- </ul></div>
- </li>
- <li class="listitem">
- 2
- <div class="itemizedlist"><ul class="itemizedlist" type="disc">
- <li class="listitem">
- 2.a
- </li>
- <li class="listitem">
- 2.b
- <div class="orderedlist"><ol class="orderedlist" type="a">
- <li class="listitem">
- 2.b.1
- </li>
- <li class="listitem">
- 2.b.2
- <div class="itemizedlist"><ul class="itemizedlist" type="circle">
- <li class="listitem">
- 2.b.2.a
- </li>
- <li class="listitem">
- 2.b.2.b
- </li>
- </ul></div>
- </li>
- </ol></div>
- </li>
- </ul></div>
- </li>
- </ol></div>
- </div>
- <div class="section">
- <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">
- <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="id769721"></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;α,β) = x<sup>α - 1</sup> (1 - x)<sup>β -1</sup> / B(α, β)
- </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>
- </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/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="images.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a>
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