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  25 <div class="refentry">
  26 <a name="boost.accumulators.impl.variance_impl"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Struct template variance_impl</span></h2>
  29 <p>boost::accumulators::impl::variance_impl &#8212; Iterative calculation of variance. </p>
  30 </div>
  31 <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
  32 <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics_fwd_hpp" title="Header &lt;boost/accumulators/statistics_fwd.hpp&gt;">boost/accumulators/statistics_fwd.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</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">&gt;</span>
  35 <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>
  36   <span class="comment">// <a class="link" href="variance_impl.html#boost.accumulators.impl.variance_implconstruct-copy-destruct">construct/copy/destruct</a></span>
  37   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</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">&amp;</span><span class="special">)</span><span class="special">;</span>
  38
  39   <span class="comment">// <a class="link" href="variance_impl.html#idp67214592-bb">public member functions</a></span>
  40   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</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">&amp;</span><span class="special">)</span><span class="special">;</span>
  41   <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>
  42 <span class="special">}</span><span class="special">;</span></pre></div>
  43 <div class="refsect1">
  44 <a name="idp111274800"></a><h2>Description</h2>
  45 <p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators//form_61.png"></span> according to the formula </p>
  46 <div class="equation">
  47 <a name="idp111277968"></a><p class="title"><b>Equation&#160;1.31.&#160;</b></p>
  48 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_62.png" align="middle"></div></div>
  49 </div>
  50 <p><br class="equation-break"> where </p>
  51 <div class="equation">
  52 <a name="idp111281008"></a><p class="title"><b>Equation&#160;1.32.&#160;</b></p>
  53 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_60.png" align="middle"></div></div>
  54 </div>
  55 <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>
  56 <p>Note that the sample variance is not defined for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_63.png"></span>.</p>
  57 <p>A simplification can be obtained by the approximate recursion </p>
  58 <div class="equation">
  59 <a name="idp111289248"></a><p class="title"><b>Equation&#160;1.33.&#160;</b></p>
  60 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_64.png" align="middle"></div></div>
  61 </div>
  62 <p><br class="equation-break"> because the difference </p>
  63 <div class="equation">
  64 <a name="idp111292208"></a><p class="title"><b>Equation&#160;1.34.&#160;</b></p>
  65 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_65.png" align="middle"></div></div>
  66 </div>
  67 <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>
  68 <div class="refsect2">
  69 <a name="idp111300032"></a><h3>
  70 <a name="boost.accumulators.impl.variance_implconstruct-copy-destruct"></a><code class="computeroutput">variance_impl</code>
  71         public
  72        construct/copy/destruct</h3>
  73 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</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">&amp;</span> args<span class="special">)</span><span class="special">;</span></pre></li></ol></div>
  74 </div>
  75 <div class="refsect2">
  76 <a name="idp111310704"></a><h3>
  77 <a name="idp67214592-bb"></a><code class="computeroutput">variance_impl</code> public member functions</h3>
  78 <div class="orderedlist"><ol class="orderedlist" type="1">
  79 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</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">&amp;</span> args<span class="special">)</span><span class="special">;</span></pre></li>
  80 <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>
  81 </ol></div>
  82 </div>
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  87 <td align="right"><div class="copyright-footer">Copyright &#169; 2005, 2006 Eric Niebler<p>
  88         Distributed under the Boost Software License, Version 1.0. (See accompanying
  89         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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