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diff --git a/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html b/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html deleted file mode 100644 index 927a61acd7..0000000000 --- a/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html +++ /dev/null @@ -1,118 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> -<html> -<head> -<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> -<title>Struct template peaks_over_threshold_impl</title> -<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> -<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> -<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.peaks_over_threshold_hpp" title="Header <boost/accumulators/statistics/peaks_over_threshold.hpp>"> -<link rel="prev" href="../extract/peaks_over_threshold.html" title="Global peaks_over_threshold"> -<link rel="next" href="../tag/abstract_peaks_idp65279920.html" title="Struct abstract_peaks_over_threshold"> -</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/peaks_over_threshold.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.peaks_over_threshold_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/abstract_peaks_idp65279920.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> -</div> -<div class="refentry"> -<a name="boost.accumulators.impl.peaks_over_threshold_impl"></a><div class="titlepage"></div> -<div class="refnamediv"> -<h2><span class="refentrytitle">Struct template peaks_over_threshold_impl</span></h2> -<p>boost::accumulators::impl::peaks_over_threshold_impl — Peaks over Threshold Method for Quantile and Tail Mean 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.peaks_over_threshold_hpp" title="Header <boost/accumulators/statistics/peaks_over_threshold.hpp>">boost/accumulators/statistics/peaks_over_threshold.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> LeftRight<span class="special">></span> -<span class="keyword">struct</span> <a class="link" href="peaks_over_threshold_impl.html" title="Struct template peaks_over_threshold_impl">peaks_over_threshold_impl</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">accumulator_base</span> <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">fdiv</span><span class="special"><</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="special">></span><span class="special">::</span><span class="identifier">result_type</span> <a name="boost.accumulators.impl.peaks_over_threshold_impl.float_type"></a><span class="identifier">float_type</span><span class="special">;</span> - <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">tuple</span><span class="special"><</span> <span class="identifier">float_type</span><span class="special">,</span> <span class="identifier">float_type</span><span class="special">,</span> <span class="identifier">float_type</span> <span class="special">></span> <a name="boost.accumulators.impl.peaks_over_threshold_impl.result_type"></a><span class="identifier">result_type</span><span class="special">;</span> - <span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span> <span class="identifier">is_same</span><span class="special"><</span> <span class="identifier">LeftRight</span><span class="special">,</span> <a class="link" href="../left.html" title="Struct left">left</a> <span class="special">></span><span class="special">::</span><span class="identifier">value</span><span class="special">?</span><span class="special">-</span><span class="number">1</span><span class="special">:</span><span class="number">1</span> <span class="special">></span> <a name="boost.accumulators.impl.peaks_over_threshold_impl.sign"></a><span class="identifier">sign</span><span class="special">;</span> - - <span class="comment">// <a class="link" href="peaks_over_threshold_impl.html#boost.accumulators.impl.peaks_over_threshold_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="peaks_over_threshold_impl.html#idp65277216-bb"><span class="identifier">peaks_over_threshold_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="peaks_over_threshold_impl.html#idp65271456-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="peaks_over_threshold_impl.html#idp65272016-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="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="peaks_over_threshold_impl.html#idp65274400-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="idp101996816"></a><h2>Description</h2> -<p>According to the theorem of Pickands-Balkema-de Haan, the distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_14.png"></span> of the excesses <span class="inlinemediaobject"><img src="../../../images/accumulators//form_15.png"></span> over some sufficiently high threshold <span class="inlinemediaobject"><img src="../../../images/accumulators//form_16.png"></span> of a distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_17.png"></span> may be approximated by a generalized Pareto distribution </p> -<div class="equation"> -<a name="idp102007120"></a><p class="title"><b>Equation 1.1. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_18.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> with suitable parameters <span class="inlinemediaobject"><img src="../../../images/accumulators//form_13.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_19.png"></span> that can be estimated, e.g., with the method of moments, cf. Hosking and Wallis (1987), </p> -<div class="equation"> -<a name="idp102015856"></a><p class="title"><b>Equation 1.2. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_20.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> <span class="inlinemediaobject"><img src="../../../images/accumulators//form_21.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_22.png"></span> being the empirical mean and variance of the samples over the threshold <span class="inlinemediaobject"><img src="../../../images/accumulators//form_16.png"></span>. Equivalently, the distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_23.png"></span> of the exceedances <span class="inlinemediaobject"><img src="../../../images/accumulators//form_24.png"></span> can be approximated by <span class="inlinemediaobject"><img src="../../../images/accumulators//form_25.png"></span>. Since for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_26.png"></span> the distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_17.png"></span> can be written as </p> -<div class="equation"> -<a name="idp102038608"></a><p class="title"><b>Equation 1.3. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_27.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> and the probability <span class="inlinemediaobject"><img src="../../../images/accumulators//form_28.png"></span> can be approximated by the empirical distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_29.png"></span> evaluated at <span class="inlinemediaobject"><img src="../../../images/accumulators//form_16.png"></span>, an estimator of <span class="inlinemediaobject"><img src="../../../images/accumulators//form_17.png"></span> is given by </p> -<div class="equation"> -<a name="idp102051168"></a><p class="title"><b>Equation 1.4. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_30.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> It can be shown that <span class="inlinemediaobject"><img src="../../../images/accumulators//form_31.png"></span> is a generalized Pareto distribution <span class="inlinemediaobject"><img src="../../../images/accumulators//form_32.png"></span> with <span class="inlinemediaobject"><img src="../../../images/accumulators//form_33.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_34.png"></span>. By inverting <span class="inlinemediaobject"><img src="../../../images/accumulators//form_31.png"></span>, one obtains an estimator for the <span class="inlinemediaobject"><img src="../../../images/accumulators//form_35.png"></span>-quantile, </p> -<div class="equation"> -<a name="idp102068768"></a><p class="title"><b>Equation 1.5. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_36.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> and similarly an estimator for the (coherent) tail mean, </p> -<div class="equation"> -<a name="idp102071792"></a><p class="title"><b>Equation 1.6. </b></p> -<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_37.png" align="middle"></div></div> -</div> -<p><br class="equation-break"> cf. McNeil and Frey (2000).</p> -<p>Note that in case extreme values of the left tail are fitted, the distribution is mirrored with respect to the <span class="inlinemediaobject"><img src="../../../images/accumulators//form_38.png"></span> axis such that the left tail can be treated as a right tail. The computed fit parameters thus define the Pareto distribution that fits the mirrored left tail. When quantities like a quantile or a tail mean are computed using the fit parameters obtained from the mirrored data, the result is mirrored back, yielding the correct result.</p> -<p>For further details, see</p> -<p>J. R. M. Hosking and J. R. Wallis, Parameter and quantile estimation for the generalized Pareto distribution, Technometrics, Volume 29, 1987, p. 339-349</p> -<p>A. J. McNeil and R. Frey, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, Journal of Empirical Finance, Volume 7, 2000, p. 271-300</p> -<p> -</p> -<div class="refsect2"> -<a name="idp102079344"></a><h3> -<a name="boost.accumulators.impl.peaks_over_threshold_implconstruct-copy-destruct"></a><code class="computeroutput">peaks_over_threshold_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="idp65277216-bb"></a><span class="identifier">peaks_over_threshold_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="idp102089968"></a><h3> -<a name="idp65271456-bb"></a><code class="computeroutput">peaks_over_threshold_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="idp65272016-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="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="idp65274400-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/peaks_over_threshold.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.peaks_over_threshold_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/abstract_peaks_idp65279920.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> -</div> -</body> -</html> |