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Diffstat (limited to 'doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html')
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1 files changed, 21 insertions, 20 deletions
diff --git a/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html b/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html index 36e9e10187..927a61acd7 100644 --- a/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html +++ b/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html @@ -1,3 +1,4 @@ +<!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"> @@ -7,7 +8,7 @@ <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_idp58594944.html" title="Struct abstract_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> @@ -20,7 +21,7 @@ </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_idp58594944.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +<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> @@ -39,42 +40,42 @@ <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#idp58592240-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="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#idp58586480-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#idp58587040-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#idp58589424-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="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="idp93971536"></a><h2>Description</h2> +<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="idp93982064"></a><p class="title"><b>Equation 1.1. </b></p> +<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="idp93990800"></a><p class="title"><b>Equation 1.2. </b></p> +<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="idp94013552"></a><p class="title"><b>Equation 1.3. </b></p> +<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="idp94026112"></a><p class="title"><b>Equation 1.4. </b></p> +<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="idp94043712"></a><p class="title"><b>Equation 1.5. </b></p> +<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="idp94046736"></a><p class="title"><b>Equation 1.6. </b></p> +<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> @@ -85,18 +86,18 @@ <p> </p> <div class="refsect2"> -<a name="idp94054240"></a><h3> +<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="idp58592240-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 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="idp94064928"></a><h3> -<a name="idp58586480-bb"></a><code class="computeroutput">peaks_over_threshold_impl</code> public member functions</h3> +<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="idp58587040-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="idp58589424-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> +<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> @@ -111,7 +112,7 @@ </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_idp58594944.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +<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> |