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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>
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<td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009 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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