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<h2><span class="refentrytitle">Struct template variance_impl</span></h2>
<p>boost::accumulators::impl::variance_impl — Iterative calculation of variance. </p>
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<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
<div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics_fwd_hpp" title="Header <boost/accumulators/statistics_fwd.hpp>">boost/accumulators/statistics_fwd.hpp</a>>
</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Sample<span class="special">,</span> <span class="keyword">typename</span> MeanFeature<span class="special">,</span> <span class="keyword">typename</span> Tag<span class="special">></span>
<span class="keyword">struct</span> <a class="link" href="variance_impl.html" title="Struct template variance_impl">variance_impl</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">accumulator_base</span> <span class="special">{</span>
<span class="comment">// <a class="link" href="variance_impl.html#boost.accumulators.impl.variance_implconstruct-copy-destruct">construct/copy/destruct</a></span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <a class="link" href="variance_impl.html#idp67219504-bb"><span class="identifier">variance_impl</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span>
<span class="comment">// <a class="link" href="variance_impl.html#idp67214592-bb">public member functions</a></span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="keyword">void</span> <a class="link" href="variance_impl.html#idp67215152-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span>
<span class="identifier">result_type</span> <a class="link" href="variance_impl.html#idp67217536-bb"><span class="identifier">result</span></a><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">}</span><span class="special">;</span></pre></div>
<div class="refsect1">
<a name="idp111274800"></a><h2>Description</h2>
<p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators//form_61.png"></span> according to the formula </p>
<div class="equation">
<a name="idp111277968"></a><p class="title"><b>Equation 1.31. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_62.png" align="middle"></div></div>
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<p><br class="equation-break"> where </p>
<div class="equation">
<a name="idp111281008"></a><p class="title"><b>Equation 1.32. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_60.png" align="middle"></div></div>
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<p><br class="equation-break"> is the estimate of the sample mean and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_47.png"></span> is the number of samples.</p>
<p>Note that the sample variance is not defined for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_63.png"></span>.</p>
<p>A simplification can be obtained by the approximate recursion </p>
<div class="equation">
<a name="idp111289248"></a><p class="title"><b>Equation 1.33. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_64.png" align="middle"></div></div>
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<p><br class="equation-break"> because the difference </p>
<div class="equation">
<a name="idp111292208"></a><p class="title"><b>Equation 1.34. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_65.png" align="middle"></div></div>
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<p><br class="equation-break"> converges to zero as <span class="inlinemediaobject"><img src="../../../images/accumulators//form_66.png"></span>. However, for small <span class="inlinemediaobject"><img src="../../../images/accumulators//form_35.png"></span> the difference can be non-negligible. </p>
<div class="refsect2">
<a name="idp111300032"></a><h3>
<a name="boost.accumulators.impl.variance_implconstruct-copy-destruct"></a><code class="computeroutput">variance_impl</code>
public
construct/copy/destruct</h3>
<div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <a name="idp67219504-bb"></a><span class="identifier">variance_impl</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> args<span class="special">)</span><span class="special">;</span></pre></li></ol></div>
</div>
<div class="refsect2">
<a name="idp111310704"></a><h3>
<a name="idp67214592-bb"></a><code class="computeroutput">variance_impl</code> public member functions</h3>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="keyword">void</span> <a name="idp67215152-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> args<span class="special">)</span><span class="special">;</span></pre></li>
<li class="listitem"><pre class="literallayout"><span class="identifier">result_type</span> <a name="idp67217536-bb"></a><span class="identifier">result</span><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li>
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<td align="right"><div class="copyright-footer">Copyright © 2005, 2006 Eric Niebler<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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