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 <h2 title="Class LevyDistribution" class="title">Class LevyDistribution</h2>
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 <li>org.apache.commons.math3.distribution.LevyDistribution</li>
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 <dd><a href="http://docs.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a>, <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</a></dd>
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 <br>
 <pre>public class <span class="strong">LevyDistribution</span>
 extends <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></pre>
 <div class="block">This class implements the <a href="http://en.wikipedia.org/wiki/L%C3%A9vy_distribution">
  L&eacute;vy distribution</a>.</div>
 <dl><dt><span class="strong">Since:</span></dt>
   <dd>3.2</dd>
 <dt><span class="strong">Version:</span></dt>
   <dd>$Id: LevyDistribution.java 1533974 2013-10-20 20:42:41Z psteitz $</dd>
 <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.LevyDistribution">Serialized Form</a></dd></dl>
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 <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#random">random</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#randomData">randomData</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#SOLVER_DEFAULT_ABSOLUTE_ACCURACY">SOLVER_DEFAULT_ABSOLUTE_ACCURACY</a></code></li>
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 <caption><span>Constructors</span><span class="tabEnd">&nbsp;</span></caption>
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 <th class="colOne" scope="col">Constructor and Description</th>
 </tr>
 <tr class="altColor">
 <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#LevyDistribution(org.apache.commons.math3.random.RandomGenerator, double, double)">LevyDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                 double&nbsp;mu,
                 double&nbsp;c)</code>
 <div class="block">Creates a LevyDistribution.</div>
 </td>
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 <caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
 <tr>
 <th class="colFirst" scope="col">Modifier and Type</th>
 <th class="colLast" scope="col">Method and Description</th>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#cumulativeProbability(double)">cumulativeProbability</a></strong>(double&nbsp;x)</code>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X &lt;= x)</code>.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#density(double)">density</a></strong>(double&nbsp;x)</code>
 <div class="block">Returns the probability density function (PDF) of this distribution
  evaluated at the specified point <code>x</code>.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getLocation()">getLocation</a></strong>()</code>
 <div class="block">Get the location parameter of the distribution.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getNumericalMean()">getNumericalMean</a></strong>()</code>
 <div class="block">Use this method to get the numerical value of the mean of this
  distribution.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getNumericalVariance()">getNumericalVariance</a></strong>()</code>
 <div class="block">Use this method to get the numerical value of the variance of this
  distribution.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getScale()">getScale</a></strong>()</code>
 <div class="block">Get the scale parameter of the distribution.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code>
 <div class="block">Access the lower bound of the support.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#getSupportUpperBound()">getSupportUpperBound</a></strong>()</code>
 <div class="block">Access the upper bound of the support.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a></strong>(double&nbsp;p)</code>
 <div class="block">Computes the quantile function of this distribution.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>boolean</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#isSupportConnected()">isSupportConnected</a></strong>()</code>
 <div class="block">Use this method to get information about whether the support is connected,
  i.e.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>boolean</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#isSupportLowerBoundInclusive()">isSupportLowerBoundInclusive</a></strong>()</code>
 <div class="block">Whether or not the lower bound of support is in the domain of the density
  function.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>boolean</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#isSupportUpperBoundInclusive()">isSupportUpperBoundInclusive</a></strong>()</code>
 <div class="block">Whether or not the upper bound of support is in the domain of the density
  function.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#logDensity(double)">logDensity</a></strong>(double&nbsp;x)</code>
 <div class="block">Returns the natural logarithm of the probability density function (PDF) of this distribution
  evaluated at the specified point <code>x</code>.</div>
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 <h4>LevyDistribution</h4>
 <pre>public&nbsp;LevyDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                 double&nbsp;mu,
                 double&nbsp;c)</pre>
 <div class="block">Creates a LevyDistribution.</div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - random generator to be used for sampling</dd><dd><code>mu</code> - location</dd><dd><code>c</code> - scale parameter</dd></dl>
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 <h4>density</h4>
 <pre>public&nbsp;double&nbsp;density(double&nbsp;x)</pre>
 <div class="block">Returns the probability density function (PDF) of this distribution
  evaluated at the specified point <code>x</code>. In general, the PDF is
  the derivative of the <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double)"><code>CDF</code></a>.
  If the derivative does not exist at <code>x</code>, then an appropriate
  replacement should be returned, e.g. <code>Double.POSITIVE_INFINITY</code>,
  <code>Double.NaN</code>, or  the limit inferior or limit superior of the
  difference quotient.
  <p>
  From Wikipedia: The probability density function of the L&eacute;vy distribution
  over the domain is
  </p>
  <pre>
  f(x; &mu;, c) = &radic;(c / 2&pi;) * e<sup>-c / 2 (x - &mu;)</sup> / (x - &mu;)<sup>3/2</sup>
  </pre>
  <p>
  For this distribution, <code>X</code>, this method returns <code>P(X &lt; x)</code>.
  If <code>x</code> is less than location parameter &mu;, <code>Double.NaN</code> is
  returned, as in these cases the distribution is not defined.
  </p></div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PDF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the value of the probability density function at point <code>x</code></dd></dl>
 </li>
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 <pre>public&nbsp;double&nbsp;logDensity(double&nbsp;x)</pre>
 <div class="block">Returns the natural logarithm of the probability density function (PDF) of this distribution
  evaluated at the specified point <code>x</code>. In general, the PDF is the derivative of the
  <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double)"><code>CDF</code></a>. If the derivative does not exist at <code>x</code>,
  then an appropriate replacement should be returned, e.g. <code>Double.POSITIVE_INFINITY</code>,
  <code>Double.NaN</code>, or the limit inferior or limit superior of the difference quotient. Note
  that due to the floating point precision and under/overflow issues, this method will for some
  distributions be more precise and faster than computing the logarithm of
  <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#density(double)"><code>RealDistribution.density(double)</code></a>. The default implementation simply computes the logarithm of
  <code>density(x)</code>.

  See documentation of <a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html#density(double)"><code>density(double)</code></a> for computation details.</div>
 <dl>
 <dt><strong>Overrides:</strong></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#logDensity(double)">logDensity</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd>
 <dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PDF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the logarithm of the value of the probability density function at point <code>x</code></dd></dl>
 </li>
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 <h4>cumulativeProbability</h4>
 <pre>public&nbsp;double&nbsp;cumulativeProbability(double&nbsp;x)</pre>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X &lt;= x)</code>. In other
  words, this method represents the (cumulative) distribution function
  (CDF) for this distribution.
  <p>
  From Wikipedia: the cumulative distribution function is
  </p>
  <pre>
  f(x; u, c) = erfc (&radic; (c / 2 (x - u )))
  </pre></div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the CDF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the probability that a random variable with this
  distribution takes a value less than or equal to <code>x</code></dd></dl>
 </li>
 </ul>
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 <h4>inverseCumulativeProbability</h4>
 <pre>public&nbsp;double&nbsp;inverseCumulativeProbability(double&nbsp;p)
                                     throws <a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></pre>
 <div class="block">Computes the quantile function of this distribution. For a random
  variable <code>X</code> distributed according to this distribution, the
  returned value is
  <ul>
  <li><code>inf{x in R | P(X<=x) >= p}</code> for <code>0 &lt; p &lt;= 1</code>,</li>
  <li><code>inf{x in R | P(X<=x) > 0}</code> for <code>p = 0</code>.</li>
  </ul>

  The default implementation returns
  <ul>
  <li><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#getSupportLowerBound()"><code>RealDistribution.getSupportLowerBound()</code></a> for <code>p = 0</code>,</li>
  <li><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#getSupportUpperBound()"><code>RealDistribution.getSupportUpperBound()</code></a> for <code>p = 1</code>.</li>
  </ul></div>
 <dl>
 <dt><strong>Specified by:</strong></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</a></code></dd>
 <dt><strong>Overrides:</strong></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd>
 <dt><span class="strong">Parameters:</span></dt><dd><code>p</code> - the cumulative probability</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the smallest <code>p</code>-quantile of this distribution
  (largest 0-quantile for <code>p = 0</code>)</dd>
 <dt><span class="strong">Throws:</span></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/exception/OutOfRangeException.html" title="class in org.apache.commons.math3.exception">OutOfRangeException</a></code> - if <code>p &lt; 0</code> or <code>p &gt; 1</code></dd></dl>
 </li>
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 <h4>getScale</h4>
 <pre>public&nbsp;double&nbsp;getScale()</pre>
 <div class="block">Get the scale parameter of the distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>scale parameter of the distribution</dd></dl>
 </li>
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 <a name="getLocation()">
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 <h4>getLocation</h4>
 <pre>public&nbsp;double&nbsp;getLocation()</pre>
 <div class="block">Get the location parameter of the distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>location parameter of the distribution</dd></dl>
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 <pre>public&nbsp;double&nbsp;getNumericalMean()</pre>
 <div class="block">Use this method to get the numerical value of the mean of this
  distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the mean or <code>Double.NaN</code> if it is not defined</dd></dl>
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 <pre>public&nbsp;double&nbsp;getNumericalVariance()</pre>
 <div class="block">Use this method to get the numerical value of the variance of this
  distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the variance (possibly <code>Double.POSITIVE_INFINITY</code> as
  for certain cases in <a href="../../../../../org/apache/commons/math3/distribution/TDistribution.html" title="class in org.apache.commons.math3.distribution"><code>TDistribution</code></a>) or <code>Double.NaN</code> if it
  is not defined</dd></dl>
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 <pre>public&nbsp;double&nbsp;getSupportLowerBound()</pre>
 <div class="block">Access the lower bound of the support. This method must return the same
  value as <code>inverseCumulativeProbability(0)</code>. In other words, this
  method must return
  <p><code>inf {x in R | P(X <= x) > 0}</code>.</p></div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>lower bound of the support (might be
  <code>Double.NEGATIVE_INFINITY</code>)</dd></dl>
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 <pre>public&nbsp;double&nbsp;getSupportUpperBound()</pre>
 <div class="block">Access the upper bound of the support. This method must return the same
  value as <code>inverseCumulativeProbability(1)</code>. In other words, this
  method must return
  <p><code>inf {x in R | P(X <= x) = 1}</code>.</p></div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support (might be
  <code>Double.POSITIVE_INFINITY</code>)</dd></dl>
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 <pre>public&nbsp;boolean&nbsp;isSupportLowerBoundInclusive()</pre>
 <div class="block">Whether or not the lower bound of support is in the domain of the density
  function.  Returns true iff <code>getSupporLowerBound()</code> is finite and
  <code>density(getSupportLowerBound())</code> returns a non-NaN, non-infinite
  value.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>true if the lower bound of support is finite and the density
  function returns a non-NaN, non-infinite value there</dd></dl>
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 <pre>public&nbsp;boolean&nbsp;isSupportUpperBoundInclusive()</pre>
 <div class="block">Whether or not the upper bound of support is in the domain of the density
  function.  Returns true iff <code>getSupportUpperBound()</code> is finite and
  <code>density(getSupportUpperBound())</code> returns a non-NaN, non-infinite
  value.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>true if the upper bound of support is finite and the density
  function returns a non-NaN, non-infinite value there</dd></dl>
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 <pre>public&nbsp;boolean&nbsp;isSupportConnected()</pre>
 <div class="block">Use this method to get information about whether the support is connected,
  i.e. whether all values between the lower and upper bound of the support
  are included in the support.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>whether the support is connected or not</dd></dl>
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