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<title>Conceptual Requirements for Distribution Types</title>
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<div class="section">
<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 22. 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>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, 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>)
</p>
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