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- <title>Conceptual Requirements for Distribution Types</title>
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- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="math_toolkit.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for
- Distribution Types</a>
- </h2></div></div></div>
- <p>
- A <span class="emphasis"><em>DistributionType</em></span> is a type that implements the following
- conceptual requirements, and encapsulates a statistical distribution.
- </p>
- <p>
- Please note that this documentation should not be used as a substitute for
- the <a class="link" href="dist_ref.html" title="Statistical Distributions Reference">reference documentation</a>, and
- <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">tutorial</a> of the statistical distributions.
- </p>
- <p>
- In the following table, <span class="emphasis"><em>d</em></span> is an object of type <code class="computeroutput"><span class="identifier">DistributionType</span></code>, <span class="emphasis"><em>cd</em></span>
- is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">DistributionType</span></code>
- and <span class="emphasis"><em>cr</em></span> is an object of a type convertible to <code class="computeroutput"><span class="identifier">RealType</span></code>.
- </p>
- <div class="informaltable"><table class="table">
- <colgroup>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- <p>
- Expression
- </p>
- </th>
- <th>
- <p>
- Result Type
- </p>
- </th>
- <th>
- <p>
- Notes
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- DistributionType::value_type
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- The real-number type <span class="emphasis"><em>RealType</em></span> upon which the
- distribution operates.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- DistributionType::policy_type
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- The <a class="link" href="../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a> to use when evaluating functions
- that depend on this distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- d = cd
- </p>
- </td>
- <td>
- <p>
- Distribution&
- </p>
- </td>
- <td>
- <p>
- Distribution types are assignable.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Distribution(cd)
- </p>
- </td>
- <td>
- <p>
- Distribution
- </p>
- </td>
- <td>
- <p>
- Distribution types are copy constructible.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- pdf(cd, cr)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the PDF of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- cdf(cd, cr)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the CDF of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- cdf(complement(cd, cr))
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the complement of the CDF of the distribution, the same as:
- <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="identifier">cr</span><span class="special">)</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- quantile(cd, cr)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the quantile (or percentile) of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- quantile(complement(cd, cr))
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the quantile (or percentile) of the distribution, starting
- from the complement of the probability, the same as: <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="number">1</span><span class="special">-</span><span class="identifier">cr</span><span class="special">)</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- chf(cd, cr)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the cumulative hazard function of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- hazard(cd, cr)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the hazard function of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- kurtosis(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the kurtosis of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- kurtosis_excess(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the kurtosis excess of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- mean(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the mean of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- mode(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the mode of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- skewness(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the skewness of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- standard_deviation(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the standard deviation of the distribution.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- variance(cd)
- </p>
- </td>
- <td>
- <p>
- RealType
- </p>
- </td>
- <td>
- <p>
- Returns the variance of the distribution.
- </p>
- </td>
- </tr>
- </tbody>
- </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 © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- Hubert Holin, Bruno Lalande, John Maddock, 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>)
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