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399 lines
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<title>Conceptual Requirements for Distribution Types</title>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for
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Distribution Types</a>
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</h2></div></div></div>
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<p>
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A <span class="emphasis"><em>DistributionType</em></span> is a type that implements the following
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conceptual requirements, and encapsulates a statistical distribution.
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</p>
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<p>
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Please note that this documentation should not be used as a substitute for
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the <a class="link" href="dist_ref.html" title="Statistical Distributions Reference">reference documentation</a>, and
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<a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">tutorial</a> of the statistical distributions.
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</p>
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<p>
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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>
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is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">DistributionType</span></code>
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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>.
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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<col>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Expression
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</p>
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</th>
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<th>
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<p>
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Result Type
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</p>
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</th>
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<th>
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<p>
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Notes
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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DistributionType::value_type
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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The real-number type <span class="emphasis"><em>RealType</em></span> upon which the
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distribution operates.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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DistributionType::policy_type
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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The <a class="link" href="../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> to use when evaluating functions
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that depend on this distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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d = cd
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</p>
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</td>
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<td>
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<p>
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Distribution&
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</p>
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</td>
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<td>
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<p>
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Distribution types are assignable.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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Distribution(cd)
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</p>
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</td>
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<td>
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<p>
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Distribution
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</p>
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</td>
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<td>
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<p>
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Distribution types are copy constructible.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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pdf(cd, cr)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the PDF of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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cdf(cd, cr)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the CDF of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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cdf(complement(cd, cr))
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the complement of the CDF of the distribution, the same as:
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<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>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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quantile(cd, cr)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the quantile (or percentile) of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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quantile(complement(cd, cr))
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the quantile (or percentile) of the distribution, starting
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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>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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chf(cd, cr)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the cumulative hazard function of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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hazard(cd, cr)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the hazard function of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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kurtosis(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the kurtosis of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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kurtosis_excess(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the kurtosis excess of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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mean(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the mean of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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mode(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the mode of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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skewness(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the skewness of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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standard_deviation(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the standard deviation of the distribution.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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variance(cd)
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</p>
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</td>
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<td>
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<p>
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RealType
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</p>
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</td>
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<td>
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<p>
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Returns the variance of the distribution.
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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</p>
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</div></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="real_concepts.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.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="archetypes.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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</html>
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