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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html">LevyFlightDistribution</a></li> </ul>
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<div class="title">LevyFlightDistribution Class Reference</div> </div>
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<p>Levy Flight distribution as needed by Boost Random.
<a href="class_quant_lib_1_1_levy_flight_distribution.html#details">More...</a></p>
<p><code>#include <ql/experimental/math/levyflightdistribution.hpp></code></p>
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Public Types</h2></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>input_type</b></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>result_type</b></td></tr>
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Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr>
<tr class="memitem:ac97ce00b941a3fafd8fe7cb5cf655669"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ac97ce00b941a3fafd8fe7cb5cf655669">LevyFlightDistribution</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ab24012a190d1249dfcd7f0169e309dee">xm</a>=1.0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ad7530134b03a24df85bd5ffe06507e87">alpha</a>=1.0)</td></tr>
<tr class="separator:ac97ce00b941a3fafd8fe7cb5cf655669"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a91f09f82b8f88fa8403cd1912a31db73"><td class="memItemLeft" align="right" valign="top"><a id="a91f09f82b8f88fa8403cd1912a31db73"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a91f09f82b8f88fa8403cd1912a31db73">LevyFlightDistribution</a> (const param_type &parm)</td></tr>
<tr class="memdesc:a91f09f82b8f88fa8403cd1912a31db73"><td class="mdescLeft"> </td><td class="mdescRight">Constructs a <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html" title="Levy Flight distribution as needed by Boost Random.">LevyFlightDistribution</a> from its parameters. <br /></td></tr>
<tr class="separator:a91f09f82b8f88fa8403cd1912a31db73"><td class="memSeparator" colspan="2"> </td></tr>
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Inspectors</h2></td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ab24012a190d1249dfcd7f0169e309dee">xm</a> () const</td></tr>
<tr class="memdesc:ab24012a190d1249dfcd7f0169e309dee"><td class="mdescLeft"> </td><td class="mdescRight">Returns the xm parameter of the distribution. <br /></td></tr>
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<tr class="memitem:ad7530134b03a24df85bd5ffe06507e87"><td class="memItemLeft" align="right" valign="top"><a id="ad7530134b03a24df85bd5ffe06507e87"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ad7530134b03a24df85bd5ffe06507e87">alpha</a> () const</td></tr>
<tr class="memdesc:ad7530134b03a24df85bd5ffe06507e87"><td class="mdescLeft"> </td><td class="mdescRight">Returns the alpha parameter of the distribution. <br /></td></tr>
<tr class="separator:ad7530134b03a24df85bd5ffe06507e87"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae3a0fd0b9ebd60b3cc70b0d85fc3cd23"><td class="memItemLeft" align="right" valign="top"><a id="ae3a0fd0b9ebd60b3cc70b0d85fc3cd23"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> min </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ae3a0fd0b9ebd60b3cc70b0d85fc3cd23">BOOST_PREVENT_MACRO_SUBSTITUTION</a> () const</td></tr>
<tr class="memdesc:ae3a0fd0b9ebd60b3cc70b0d85fc3cd23"><td class="mdescLeft"> </td><td class="mdescRight">Returns the smallest value that the distribution can produce. <br /></td></tr>
<tr class="separator:ae3a0fd0b9ebd60b3cc70b0d85fc3cd23"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad0b33b8c3c913b3c538c547b39455c02"><td class="memItemLeft" align="right" valign="top"><a id="ad0b33b8c3c913b3c538c547b39455c02"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> max </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ad0b33b8c3c913b3c538c547b39455c02">BOOST_PREVENT_MACRO_SUBSTITUTION</a> () const</td></tr>
<tr class="memdesc:ad0b33b8c3c913b3c538c547b39455c02"><td class="mdescLeft"> </td><td class="mdescRight">Returns the largest value that the distribution can produce. <br /></td></tr>
<tr class="separator:ad0b33b8c3c913b3c538c547b39455c02"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a20c60ba1fadff5aca3fcc5f56b47ec60"><td class="memItemLeft" align="right" valign="top"><a id="a20c60ba1fadff5aca3fcc5f56b47ec60"></a>
param_type </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a20c60ba1fadff5aca3fcc5f56b47ec60">param</a> () const</td></tr>
<tr class="memdesc:a20c60ba1fadff5aca3fcc5f56b47ec60"><td class="mdescLeft"> </td><td class="mdescRight">Returns the parameters of the distribution. <br /></td></tr>
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<tr class="memitem:a52ea969cdb67e40342cbef2f6d397010"><td class="memItemLeft" align="right" valign="top"><a id="a52ea969cdb67e40342cbef2f6d397010"></a>
void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a52ea969cdb67e40342cbef2f6d397010">param</a> (const param_type &parm)</td></tr>
<tr class="memdesc:a52ea969cdb67e40342cbef2f6d397010"><td class="mdescLeft"> </td><td class="mdescRight">Sets the parameters of the distribution. <br /></td></tr>
<tr class="separator:a52ea969cdb67e40342cbef2f6d397010"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad20897c5c8bd47f5d4005989bead0e55"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#ad20897c5c8bd47f5d4005989bead0e55">reset</a> ()</td></tr>
<tr class="separator:ad20897c5c8bd47f5d4005989bead0e55"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a3a9a172e68da099a44c298bdbb2761d3"><td class="memItemLeft" align="right" valign="top"><a id="a3a9a172e68da099a44c298bdbb2761d3"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a3a9a172e68da099a44c298bdbb2761d3">operator()</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const</td></tr>
<tr class="memdesc:a3a9a172e68da099a44c298bdbb2761d3"><td class="mdescLeft"> </td><td class="mdescRight">Returns the value of the pdf for x. <br /></td></tr>
<tr class="separator:a3a9a172e68da099a44c298bdbb2761d3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a03a7c4384945167ab3affa53a7aef382"><td class="memTemplParams" colspan="2">template<class Engine > </td></tr>
<tr class="memitem:a03a7c4384945167ab3affa53a7aef382"><td class="memTemplItemLeft" align="right" valign="top">result_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a03a7c4384945167ab3affa53a7aef382">operator()</a> (Engine &eng) const</td></tr>
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<tr class="memitem:a95c3755d461e4af09c1eaeca0dda029c"><td class="memTemplParams" colspan="2">template<class Engine > </td></tr>
<tr class="memitem:a95c3755d461e4af09c1eaeca0dda029c"><td class="memTemplItemLeft" align="right" valign="top">result_type </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a95c3755d461e4af09c1eaeca0dda029c">operator()</a> (Engine &eng, const param_type &parm) const</td></tr>
<tr class="separator:a95c3755d461e4af09c1eaeca0dda029c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a65179b64c0c0068b91c3aa5dd6e2aefd"><td class="memItemLeft" align="right" valign="top"><a id="a65179b64c0c0068b91c3aa5dd6e2aefd"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a65179b64c0c0068b91c3aa5dd6e2aefd">BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR</a> (os, <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html">LevyFlightDistribution</a>, ed)</td></tr>
<tr class="memdesc:a65179b64c0c0068b91c3aa5dd6e2aefd"><td class="mdescLeft"> </td><td class="mdescRight">Writes the distribution to a std::ostream. <br /></td></tr>
<tr class="separator:a65179b64c0c0068b91c3aa5dd6e2aefd"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a473089fd3dadcd3a5442aa3f53fa1a24"><td class="memItemLeft" align="right" valign="top"><a id="a473089fd3dadcd3a5442aa3f53fa1a24"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a473089fd3dadcd3a5442aa3f53fa1a24">BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR</a> (is, <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html">LevyFlightDistribution</a>, ed)</td></tr>
<tr class="memdesc:a473089fd3dadcd3a5442aa3f53fa1a24"><td class="mdescLeft"> </td><td class="mdescRight">Reads the distribution from a std::istream. <br /></td></tr>
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<tr class="memitem:a1883c52360af1a770313a908ebf11f30"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html#a1883c52360af1a770313a908ebf11f30">BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR</a> (<a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html">LevyFlightDistribution</a>, lhs, rhs)</td></tr>
<tr class="separator:a1883c52360af1a770313a908ebf11f30"><td class="memSeparator" colspan="2"> </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Levy Flight distribution as needed by Boost Random. </p>
<p>The levy flight distribution is a random distribution with the following form: </p><p class="formulaDsp">
\[ p(x) = \frac{\alpha x_m^{\alpha}}{x^{\alpha+1}} \]
</p>
<p> with support over \( x \in [x_m, \infty) \) and the parameter \( \alpha > 0 \).</p>
<p>Levy Flight is normally defined as \( x_m = 1 \) and \( 0 < \alpha < 2 \), which is where \( p(x) \) has an infinite variance. However, the more general version, known as Pareto Type I, is well defined for \( \alpha > 2 \), so the current implementation does not restrict \( \alpha \) to be smaller than 2. </p>
</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
<a id="ac97ce00b941a3fafd8fe7cb5cf655669"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac97ce00b941a3fafd8fe7cb5cf655669">◆ </a></span>LevyFlightDistribution()</h2>
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<td class="memname"><a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html">LevyFlightDistribution</a> </td>
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<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>xm</em> = <code>1.0</code>, </td>
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<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>alpha</em> = <code>1.0</code> </td>
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<p>Constructs a <a class="el" href="class_quant_lib_1_1_levy_flight_distribution.html" title="Levy Flight distribution as needed by Boost Random.">LevyFlightDistribution</a> with a given xm and alpha Requires: alpha > 0 </p>
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<h2 class="groupheader">Member Function Documentation</h2>
<a id="ad20897c5c8bd47f5d4005989bead0e55"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad20897c5c8bd47f5d4005989bead0e55">◆ </a></span>reset()</h2>
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<td class="memname">void reset </td>
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<p>Effects: Subsequent uses of the distribution do not depend on values produced by any engine prior to invoking reset. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a03a7c4384945167ab3affa53a7aef382">◆ </a></span>operator()() <span class="overload">[1/2]</span></h2>
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<td class="memname">result_type operator() </td>
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<p>Returns a random variate distributed according to the levy flight distribution. </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a95c3755d461e4af09c1eaeca0dda029c">◆ </a></span>operator()() <span class="overload">[2/2]</span></h2>
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<td class="memname">result_type operator() </td>
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<p>Returns a random variate distributed according to the levy flight with parameters specified by parm </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a1883c52360af1a770313a908ebf11f30">◆ </a></span>BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR()</h2>
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<td class="memname">BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR </td>
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<p>Returns true iff the two distributions will produce identical sequences of values given equal generators. </p>
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