<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Struct template kurtosis_impl</title> <link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.75.2"> <link rel="home" href="../../../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> <link rel="up" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.kurtosis_hpp" title="Header <boost/accumulators/statistics/kurtosis.hpp>"> <link rel="prev" href="../extract/kurtosis.html" title="Global kurtosis"> <link rel="next" href="../tag/kurtosis.html" title="Struct kurtosis"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> <td align="center"><a href="../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../extract/kurtosis.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.kurtosis_hpp"><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="../tag/kurtosis.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> </div> <div class="refentry"> <a name="boost.accumulators.impl.kurtosis_impl"></a><div class="titlepage"></div> <div class="refnamediv"> <h2><span class="refentrytitle">Struct template kurtosis_impl</span></h2> <p>boost::accumulators::impl::kurtosis_impl — Kurtosis estimation. </p> </div> <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.kurtosis_hpp" title="Header <boost/accumulators/statistics/kurtosis.hpp>">boost/accumulators/statistics/kurtosis.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">struct</span> <a class="link" href="kurtosis_impl.html" title="Struct template kurtosis_impl">kurtosis_impl</a> <span class="special">{</span> <span class="comment">// types</span> <span class="keyword">typedef</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">average</span><span class="special"><</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="identifier">Sample</span> <span class="special">></span><span class="special">::</span><span class="identifier">result_type</span> <a name="boost.accumulators.impl.kurtosis_impl.result_type"></a><span class="identifier">result_type</span><span class="special">;</span> <span class="comment">// <a class="link" href="kurtosis_impl.html#boost.accumulators.impl.kurtosis_implconstruct-copy-destruct">construct/copy/destruct</a></span> <a class="link" href="kurtosis_impl.html#id558750-bb"><span class="identifier">kurtosis_impl</span></a><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span><span class="special">;</span> <span class="comment">// <a class="link" href="kurtosis_impl.html#id558726-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="identifier">result_type</span> <a class="link" href="kurtosis_impl.html#id558730-bb"><span class="identifier">result</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="keyword">const</span><span class="special">;</span> <span class="special">}</span><span class="special">;</span></pre></div> <div class="refsect1"> <a name="id875469"></a><h2>Description</h2> <p>The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central moment (the variance) of the samples, minus 3. The term <span class="inlinemediaobject"><img src="../../../images/accumulators/form_12.png"></span> is added in order to ensure that the normal distribution has zero kurtosis. The kurtosis can also be expressed by the simple moments:</p> <div class="equation"> <a name="id875500"></a><p class="title"><b>Equation 1.2. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators/form_13.png" align="middle"></div></div> </div> <p><br class="equation-break"></p> <p>where <span class="inlinemediaobject"><img src="../../../images/accumulators/form_14.png"></span> are the <span class="inlinemediaobject"><img src="../../../images/accumulators/form_15.png"></span>-th moment and <span class="inlinemediaobject"><img src="../../../images/accumulators/form_16.png"></span> the mean (first moment) of the <span class="inlinemediaobject"><img src="../../../images/accumulators/form_17.png"></span> samples. </p> <div class="refsect2"> <a name="id875610"></a><h3> <a name="boost.accumulators.impl.kurtosis_implconstruct-copy-destruct"></a><code class="computeroutput">kurtosis_impl</code> public construct/copy/destruct</h3> <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><a name="id558750-bb"></a><span class="identifier">kurtosis_impl</span><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span><span class="special">;</span></pre></li></ol></div> </div> <div class="refsect2"> <a name="id875664"></a><h3> <a name="id558726-bb"></a><code class="computeroutput">kurtosis_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="identifier">result_type</span> <a name="id558730-bb"></a><span class="identifier">result</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="keyword">const</span><span class="special">;</span></pre></li></ol></div> </div> </div> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <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>) </p> </div></td> </tr></table> <hr> <div class="spirit-nav"> <a accesskey="p" href="../extract/kurtosis.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.kurtosis_hpp"><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="../tag/kurtosis.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>