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<div class="subTitle">org.apache.commons.math3.distribution</div>
<h2 title="Class LogNormalDistribution" class="title">Class LogNormalDistribution</h2>
</div>
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<li>
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<li><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">org.apache.commons.math3.distribution.AbstractRealDistribution</a></li>
<li>
<ul class="inheritance">
<li>org.apache.commons.math3.distribution.LogNormalDistribution</li>
</ul>
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<dt>All Implemented Interfaces:</dt>
<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">LogNormalDistribution</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">Implementation of the log-normal (gaussian) distribution.
<p>
<strong>Parameters:</strong>
<code>X</code> is log-normally distributed if its natural logarithm <code>log(X)</code>
is normally distributed. The probability distribution function of <code>X</code>
is given by (for <code>x &gt; 0</code>)
</p>
<p>
<code>exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)</code>
</p>
<ul>
<li><code>m</code> is the <em>scale</em> parameter: this is the mean of the
normally distributed natural logarithm of this distribution,</li>
<li><code>s</code> is the <em>shape</em> parameter: this is the standard
deviation of the normally distributed natural logarithm of this
distribution.
</ul></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.0</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: LogNormalDistribution.java 1538998 2013-11-05 13:51:24Z erans $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Log-normal_distribution">
Log-normal distribution (Wikipedia)</a>,
<a href="http://mathworld.wolfram.com/LogNormalDistribution.html">
Log Normal distribution (MathWorld)</a>,
<a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.LogNormalDistribution">Serialized Form</a></dd></dl>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#DEFAULT_INVERSE_ABSOLUTE_ACCURACY">DEFAULT_INVERSE_ABSOLUTE_ACCURACY</a></strong></code>
<div class="block">Default inverse cumulative probability accuracy.</div>
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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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<th class="colOne" scope="col">Constructor and Description</th>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#LogNormalDistribution()">LogNormalDistribution</a></strong>()</code>
<div class="block">Create a log-normal distribution, where the mean and standard deviation
of the <a href="../../../../../org/apache/commons/math3/distribution/NormalDistribution.html" title="class in org.apache.commons.math3.distribution"><code>normally distributed</code></a> natural
logarithm of the log-normal distribution are equal to zero and one
respectively.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#LogNormalDistribution(double, double)">LogNormalDistribution</a></strong>(double&nbsp;scale,
double&nbsp;shape)</code>
<div class="block">Create a log-normal distribution using the specified scale and shape.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#LogNormalDistribution(double, double, double)">LogNormalDistribution</a></strong>(double&nbsp;scale,
double&nbsp;shape,
double&nbsp;inverseCumAccuracy)</code>
<div class="block">Create a log-normal distribution using the specified scale, shape and
inverse cumulative distribution accuracy.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#LogNormalDistribution(org.apache.commons.math3.random.RandomGenerator, double, double)">LogNormalDistribution</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;scale,
double&nbsp;shape)</code>
<div class="block">Creates a log-normal distribution.</div>
</td>
</tr>
<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#LogNormalDistribution(org.apache.commons.math3.random.RandomGenerator, double, double, double)">LogNormalDistribution</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;scale,
double&nbsp;shape,
double&nbsp;inverseCumAccuracy)</code>
<div class="block">Creates a log-normal distribution.</div>
</td>
</tr>
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<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/LogNormalDistribution.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/LogNormalDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</a></strong>(double&nbsp;x0,
double&nbsp;x1)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;
<div class="block"><i>See <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)"><code>RealDistribution.cumulativeProbability(double,double)</code></a></i></div>
</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/LogNormalDistribution.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="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.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/LogNormalDistribution.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/LogNormalDistribution.html#getScale()">getScale</a></strong>()</code>
<div class="block">Returns the scale parameter 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/LogNormalDistribution.html#getShape()">getShape</a></strong>()</code>
<div class="block">Returns the shape parameter of this distribution.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</a></strong>()</code>
<div class="block">Returns the solver absolute accuracy for inverse cumulative computation.</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/LogNormalDistribution.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/LogNormalDistribution.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>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.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="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.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="altColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.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="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.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>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html#probability(double, double)">probability</a></strong>(double&nbsp;x0,
double&nbsp;x1)</code>
<div class="block">For a random variable <code>X</code> whose values are distributed according
to this distribution, this method returns <code>P(x0 &lt; X &lt;= x1)</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/LogNormalDistribution.html#sample()">sample</a></strong>()</code>
<div class="block">Generate a random value sampled from this distribution.</div>
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<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double)">probability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample(int)">sample</a></code></li>
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<pre>public static final&nbsp;double DEFAULT_INVERSE_ABSOLUTE_ACCURACY</pre>
<div class="block">Default inverse cumulative probability accuracy.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.distribution.LogNormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY">Constant Field Values</a></dd></dl>
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<h4>LogNormalDistribution</h4>
<pre>public&nbsp;LogNormalDistribution()</pre>
<div class="block">Create a log-normal distribution, where the mean and standard deviation
of the <a href="../../../../../org/apache/commons/math3/distribution/NormalDistribution.html" title="class in org.apache.commons.math3.distribution"><code>normally distributed</code></a> natural
logarithm of the log-normal distribution are equal to zero and one
respectively. In other words, the scale of the returned distribution is
<code>0</code>, while its shape is <code>1</code>.</div>
</li>
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<pre>public&nbsp;LogNormalDistribution(double&nbsp;scale,
double&nbsp;shape)
throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Create a log-normal distribution using the specified scale and shape.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>scale</code> - the scale parameter of this distribution</dd><dd><code>shape</code> - the shape parameter of this distribution</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>shape &lt;= 0</code>.</dd></dl>
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<pre>public&nbsp;LogNormalDistribution(double&nbsp;scale,
double&nbsp;shape,
double&nbsp;inverseCumAccuracy)
throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Create a log-normal distribution using the specified scale, shape and
inverse cumulative distribution accuracy.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>scale</code> - the scale parameter of this distribution</dd><dd><code>shape</code> - the shape parameter of this distribution</dd><dd><code>inverseCumAccuracy</code> - Inverse cumulative probability accuracy.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>shape &lt;= 0</code>.</dd></dl>
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<pre>public&nbsp;LogNormalDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
double&nbsp;scale,
double&nbsp;shape)
throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Creates a log-normal distribution.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>scale</code> - Scale parameter of this distribution.</dd><dd><code>shape</code> - Shape parameter of this distribution.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>shape &lt;= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>3.3</dd></dl>
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<h4>LogNormalDistribution</h4>
<pre>public&nbsp;LogNormalDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
double&nbsp;scale,
double&nbsp;shape,
double&nbsp;inverseCumAccuracy)
throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
<div class="block">Creates a log-normal distribution.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>scale</code> - Scale parameter of this distribution.</dd><dd><code>shape</code> - Shape parameter of this distribution.</dd><dd><code>inverseCumAccuracy</code> - Inverse cumulative probability accuracy.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>shape &lt;= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>3.1</dd></dl>
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<h3>Method Detail</h3>
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<h4>getScale</h4>
<pre>public&nbsp;double&nbsp;getScale()</pre>
<div class="block">Returns the scale parameter of this distribution.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the scale parameter</dd></dl>
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<h4>getShape</h4>
<pre>public&nbsp;double&nbsp;getShape()</pre>
<div class="block">Returns the shape parameter of this distribution.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the shape parameter</dd></dl>
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<a name="density(double)">
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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.
For scale <code>m</code>, and shape <code>s</code> of this distribution, the PDF
is given by
<ul>
<li><code>0</code> if <code>x &lt;= 0</code>,</li>
<li><code>exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)</code>
otherwise.</li>
</ul></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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<h4>logDensity</h4>
<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/LogNormalDistribution.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>
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<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.
For scale <code>m</code>, and shape <code>s</code> of this distribution, the CDF
is given by
<ul>
<li><code>0</code> if <code>x &lt;= 0</code>,</li>
<li><code>0</code> if <code>ln(x) - m &lt; 0</code> and <code>m - ln(x) &gt; 40 * s</code>, as
in these cases the actual value is within <code>Double.MIN_VALUE</code> of 0,
<li><code>1</code> if <code>ln(x) - m &gt;= 0</code> and <code>ln(x) - m &gt; 40 * s</code>,
as in these cases the actual value is within <code>Double.MIN_VALUE</code> of
1,</li>
<li><code>0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2))</code> otherwise.</li>
</ul></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>cumulativeProbability</h4>
<pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
public&nbsp;double&nbsp;cumulativeProbability(double&nbsp;x0,
double&nbsp;x1)
throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></pre>
<div class="block"><span class="strong">Deprecated.</span>&nbsp;<i>See <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)"><code>RealDistribution.cumulativeProbability(double,double)</code></a></i></div>
<div class="block">For a random variable <code>X</code> whose values are distributed according
to this distribution, this method returns <code>P(x0 &lt; X &lt;= x1)</code>.
The default implementation uses the identity
<p><code>P(x0 &lt; X &lt;= x1) = P(X &lt;= x1) - P(X &lt;= x0)</code></p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</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#cumulativeProbability(double, double)">cumulativeProbability</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>x0</code> - the exclusive lower bound</dd><dd><code>x1</code> - the inclusive upper bound</dd>
<dt><span class="strong">Returns:</span></dt><dd>the probability that a random variable with this distribution
takes a value between <code>x0</code> and <code>x1</code>,
excluding the lower and including the upper endpoint</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>x0 &gt; x1</code></dd></dl>
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<pre>public&nbsp;double&nbsp;probability(double&nbsp;x0,
double&nbsp;x1)
throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></pre>
<div class="block">For a random variable <code>X</code> whose values are distributed according
to this distribution, this method returns <code>P(x0 &lt; X &lt;= x1)</code>.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double, double)">probability</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>x0</code> - Lower bound (excluded).</dd><dd><code>x1</code> - Upper bound (included).</dd>
<dt><span class="strong">Returns:</span></dt><dd>the probability that a random variable with this distribution
takes a value between <code>x0</code> and <code>x1</code>, excluding the lower
and including the upper endpoint.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>x0 &gt; x1</code>.
The default implementation uses the identity
<code>P(x0 &lt; X &lt;= x1) = P(X &lt;= x1) - P(X &lt;= x0)</code></dd></dl>
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<h4>getSolverAbsoluteAccuracy</h4>
<pre>protected&nbsp;double&nbsp;getSolverAbsoluteAccuracy()</pre>
<div class="block">Returns the solver absolute accuracy for inverse cumulative computation.
You can override this method in order to use a Brent solver with an
absolute accuracy different from the default.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</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">Returns:</span></dt><dd>the maximum absolute error in inverse cumulative probability estimates</dd></dl>
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<h4>getNumericalMean</h4>
<pre>public&nbsp;double&nbsp;getNumericalMean()</pre>
<div class="block">Use this method to get the numerical value of the mean of this
distribution.
For scale <code>m</code> and shape <code>s</code>, the mean is
<code>exp(m + s^2 / 2)</code>.</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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<h4>getNumericalVariance</h4>
<pre>public&nbsp;double&nbsp;getNumericalVariance()</pre>
<div class="block">Use this method to get the numerical value of the variance of this
distribution.
For scale <code>m</code> and shape <code>s</code>, the variance is
<code>(exp(s^2) - 1) * exp(2 * m + s^2)</code>.</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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<h4>getSupportLowerBound</h4>
<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>
The lower bound of the support is always 0 no matter the parameters.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>lower bound of the support (always 0)</dd></dl>
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<h4>getSupportUpperBound</h4>
<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>
The upper bound of the support is always positive infinity
no matter the parameters.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support (always
<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>
</li>
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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.
The support of this distribution is connected.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code></dd></dl>
</li>
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<h4>sample</h4>
<pre>public&nbsp;double&nbsp;sample()</pre>
<div class="block">Generate a random value sampled from this distribution.
The default implementation uses the
<a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling">
inversion method.
</a></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#sample()">sample</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#sample()">sample</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">Returns:</span></dt><dd>a random value.</dd></dl>
</li>
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