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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.using_udt.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types"> Conceptual Requirements |
| for Distribution Types</a> |
| </h3></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/dist_ref.html" title="Statistical Distributions Reference">reference documentation</a>, |
| and <a class="link" href="../dist/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="Policies">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 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 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 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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> |
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