<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Struct template weighted_kurtosis_impl</title> <link rel="stylesheet" href="../../../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.weighted_kurtosis_hpp" title="Header <boost/accumulators/statistics/weighted_kurtosis.hpp>"> <link rel="prev" href="../extract/weighted_kurtosis.html" title="Global weighted_kurtosis"> <link rel="next" href="../tag/weighted_kurtosis.html" title="Struct weighted_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/weighted_kurtosis.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.weighted_kurtosis_hpp"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../tag/weighted_kurtosis.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a> </div> <div class="refentry" title="Struct template weighted_kurtosis_impl"> <a name="boost.accumulators.impl.weighted_kurtosis_impl"></a><div class="titlepage"></div> <div class="refnamediv"> <h2><span class="refentrytitle">Struct template weighted_kurtosis_impl</span></h2> <p>boost::accumulators::impl::weighted_kurtosis_impl — Kurtosis estimation for weighted samples. </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="emphasis"><em>// In header: <<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.weighted_kurtosis_hpp" title="Header <boost/accumulators/statistics/weighted_kurtosis.hpp>">boost/accumulators/statistics/weighted_kurtosis.hpp</a>> </em></span><span class="bold"><strong>template</strong></span><<span class="bold"><strong>typename</strong></span> Sample, <span class="bold"><strong>typename</strong></span> Weight> <span class="bold"><strong>struct</strong></span> <a class="link" href="weighted_kurtosis_impl.html" title="Struct template weighted_kurtosis_impl">weighted_kurtosis_impl</a> { <span class="emphasis"><em>// types</em></span> <span class="bold"><strong>typedef</strong></span> numeric::functional::multiplies< Sample, Weight >::result_type <a name="boost.accumulators.impl.weighted_kurtosis_impl.weighted_sample"></a>weighted_sample; <span class="bold"><strong>typedef</strong></span> numeric::functional::average< weighted_sample, weighted_sample >::result_type <a name="boost.accumulators.impl.weighted_kurtosis_impl.result_type"></a>result_type; <span class="emphasis"><em>// <a class="link" href="weighted_kurtosis_impl.html#boost.accumulators.impl.weighted_kurtosis_implconstruct-copy-destruct">construct/copy/destruct</a></em></span> <a class="link" href="weighted_kurtosis_impl.html#id562714-bb">weighted_kurtosis_impl</a>(dont_care); <span class="emphasis"><em>// <a class="link" href="weighted_kurtosis_impl.html#id562690-bb">public member functions</a></em></span> <span class="bold"><strong>template</strong></span><<span class="bold"><strong>typename</strong></span> Args> <span class="type">result_type</span> <a class="link" href="weighted_kurtosis_impl.html#id562694-bb">result</a>(Args <span class="bold"><strong>const</strong></span> &) <span class="bold"><strong>const</strong></span>; };</pre></div> <div class="refsect1" title="Description"> <a name="id688956"></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="id688988"></a><p class="title"><b>Equation 1.28. </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> <p>The kurtosis estimator for weighted samples is formally identical to the estimator for unweighted samples, except that the weighted counterparts of all measures it depends on are to be taken. </p> <div class="refsect2" title="weighted_kurtosis_impl public construct/copy/destruct"> <a name="id689103"></a><h3> <a name="boost.accumulators.impl.weighted_kurtosis_implconstruct-copy-destruct"></a><code class="computeroutput">weighted_kurtosis_impl</code> public construct/copy/destruct</h3> <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><a name="id562714-bb"></a>weighted_kurtosis_impl(dont_care);</pre></li></ol></div> </div> <div class="refsect2" title="weighted_kurtosis_impl public member functions"> <a name="id689138"></a><h3> <a name="id562690-bb"></a><code class="computeroutput">weighted_kurtosis_impl</code> public member functions</h3> <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="bold"><strong>template</strong></span><<span class="bold"><strong>typename</strong></span> Args> <span class="type">result_type</span> <a name="id562694-bb"></a>result(Args <span class="bold"><strong>const</strong></span> & args) <span class="bold"><strong>const</strong></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/weighted_kurtosis.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.weighted_kurtosis_hpp"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../tag/weighted_kurtosis.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a> </div> </body> </html>