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1 files changed, 20 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 31b3265573..1c02c07fa1 100644 --- a/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html +++ b/doc/html/boost/accumulators/impl/peaks_over_threshold_impl.html @@ -8,7 +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_peak_idp413030464.html" title="Struct abstract_peaks_over_threshold"> +<link rel="next" href="../tag/abst_1_3_2_6_3_19_1_1_11_1.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> @@ -21,7 +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_peak_idp413030464.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/abst_1_3_2_6_3_19_1_1_11_1.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> @@ -40,42 +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#idp413027760-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#id-1_3_2_6_3_19_1_1_10_1_9-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#idp413022000-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#idp413022560-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#idp413024944-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#id-1_3_2_6_3_19_1_1_10_1_8-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#id-1_3_2_6_3_19_1_1_10_1_8_1-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#id-1_3_2_6_3_19_1_1_10_1_8_2-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="idp109622128"></a><h2>Description</h2> +<a name="id-1.3.2.6.3.18.4.4"></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_90.png"></span> of the excesses <span class="inlinemediaobject"><img src="../../../images/accumulators//form_91.png"></span> over some sufficiently high threshold <span class="inlinemediaobject"><img src="../../../images/accumulators//form_92.png"></span> of a distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_93.png"></span> may be approximated by a generalized Pareto distribution </p> <div class="equation"> -<a name="idp109632432"></a><p class="title"><b>Equation 1.1. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.5"></a><p class="title"><b>Equation 1.1. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_94.png" align="middle"></div></div> </div> <p><br class="equation-break"> with suitable parameters <span class="inlinemediaobject"><img src="../../../images/accumulators//form_88.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_95.png"></span> that can be estimated, e.g., with the method of moments, cf. Hosking and Wallis (1987), </p> <div class="equation"> -<a name="idp109641168"></a><p class="title"><b>Equation 1.2. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.8"></a><p class="title"><b>Equation 1.2. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_96.png" align="middle"></div></div> </div> <p><br class="equation-break"> <span class="inlinemediaobject"><img src="../../../images/accumulators//form_97.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_98.png"></span> being the empirical mean and variance of the samples over the threshold <span class="inlinemediaobject"><img src="../../../images/accumulators//form_92.png"></span>. Equivalently, the distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_99.png"></span> of the exceedances <span class="inlinemediaobject"><img src="../../../images/accumulators//form_100.png"></span> can be approximated by <span class="inlinemediaobject"><img src="../../../images/accumulators//form_101.png"></span>. Since for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_102.png"></span> the distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_93.png"></span> can be written as </p> <div class="equation"> -<a name="idp109663920"></a><p class="title"><b>Equation 1.3. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.17"></a><p class="title"><b>Equation 1.3. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_103.png" align="middle"></div></div> </div> <p><br class="equation-break"> and the probability <span class="inlinemediaobject"><img src="../../../images/accumulators//form_104.png"></span> can be approximated by the empirical distribution function <span class="inlinemediaobject"><img src="../../../images/accumulators//form_105.png"></span> evaluated at <span class="inlinemediaobject"><img src="../../../images/accumulators//form_92.png"></span>, an estimator of <span class="inlinemediaobject"><img src="../../../images/accumulators//form_93.png"></span> is given by </p> <div class="equation"> -<a name="idp109676480"></a><p class="title"><b>Equation 1.4. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.22"></a><p class="title"><b>Equation 1.4. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_106.png" align="middle"></div></div> </div> <p><br class="equation-break"> It can be shown that <span class="inlinemediaobject"><img src="../../../images/accumulators//form_107.png"></span> is a generalized Pareto distribution <span class="inlinemediaobject"><img src="../../../images/accumulators//form_108.png"></span> with <span class="inlinemediaobject"><img src="../../../images/accumulators//form_109.png"></span> and <span class="inlinemediaobject"><img src="../../../images/accumulators//form_110.png"></span>. By inverting <span class="inlinemediaobject"><img src="../../../images/accumulators//form_107.png"></span>, one obtains an estimator for the <span class="inlinemediaobject"><img src="../../../images/accumulators//form_20.png"></span>-quantile, </p> <div class="equation"> -<a name="idp109694080"></a><p class="title"><b>Equation 1.5. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.29"></a><p class="title"><b>Equation 1.5. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_111.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="idp109697104"></a><p class="title"><b>Equation 1.6. </b></p> +<a name="id-1.3.2.6.3.18.4.4.2.30"></a><p class="title"><b>Equation 1.6. </b></p> <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_85.png" align="middle"></div></div> </div> <p><br class="equation-break"> cf. McNeil and Frey (2000).</p> @@ -86,18 +86,18 @@ <p> </p> <div class="refsect2"> -<a name="idp109704656"></a><h3> +<a name="id-1.3.2.6.3.18.4.4.8"></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="idp413027760-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="id-1_3_2_6_3_19_1_1_10_1_9-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="idp109715408"></a><h3> -<a name="idp413022000-bb"></a><code class="computeroutput">peaks_over_threshold_impl</code> public member functions</h3> +<a name="id-1.3.2.6.3.18.4.4.9"></a><h3> +<a name="id-1_3_2_6_3_19_1_1_10_1_8-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="idp413022560-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="idp413024944-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="id-1_3_2_6_3_19_1_1_10_1_8_1-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="id-1_3_2_6_3_19_1_1_10_1_8_2-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> @@ -112,7 +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_peak_idp413030464.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/abst_1_3_2_6_3_19_1_1_11_1.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html> |