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+<!-- ======== START OF CLASS DATA ======== -->
+<div class="header">
+<div class="subTitle">org.apache.commons.math3.distribution</div>
+<h2 title="Interface RealDistribution" class="title">Interface RealDistribution</h2>
+</div>
+<div class="contentContainer">
+<div class="description">
+<ul class="blockList">
+<li class="blockList">
+<dl>
+<dt>All Known Implementing Classes:</dt>
+<dd><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html" title="class in org.apache.commons.math3.distribution">BetaDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/CauchyDistribution.html" title="class in org.apache.commons.math3.distribution">CauchyDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/ChiSquaredDistribution.html" title="class in org.apache.commons.math3.distribution">ChiSquaredDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/ConstantRealDistribution.html" title="class in org.apache.commons.math3.distribution">ConstantRealDistribution</a>, <a href="../../../../../org/apache/commons/math3/random/EmpiricalDistribution.html" title="class in org.apache.commons.math3.random">EmpiricalDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/EnumeratedRealDistribution.html" title="class in org.apache.commons.math3.distribution">EnumeratedRealDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/ExponentialDistribution.html" title="class in org.apache.commons.math3.distribution">ExponentialDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/FDistribution.html" title="class in org.apache.commons.math3.distribution">FDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/GammaDistribution.html" title="class in org.apache.commons.math3.distribution">GammaDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/GumbelDistribution.html" title="class in org.apache.commons.math3.distribution">GumbelDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/LaplaceDistribution.html" title="class in org.apache.commons.math3.distribution">LaplaceDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/LevyDistribution.html" title="class in org.apache.commons.math3.distribution">LevyDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/LogisticDistribution.html" title="class in org.apache.commons.math3.distribution">LogisticDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/LogNormalDistribution.html" title="class in org.apache.commons.math3.distribution">LogNormalDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/NakagamiDistribution.html" title="class in org.apache.commons.math3.distribution">NakagamiDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/NormalDistribution.html" title="class in org.apache.commons.math3.distribution">NormalDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html" title="class in org.apache.commons.math3.distribution">ParetoDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/TDistribution.html" title="class in org.apache.commons.math3.distribution">TDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/TriangularDistribution.html" title="class in org.apache.commons.math3.distribution">TriangularDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/UniformRealDistribution.html" title="class in org.apache.commons.math3.distribution">UniformRealDistribution</a>, <a href="../../../../../org/apache/commons/math3/distribution/WeibullDistribution.html" title="class in org.apache.commons.math3.distribution">WeibullDistribution</a></dd>
+</dl>
+<hr>
+<br>
+<pre>public interface <span class="strong">RealDistribution</span></pre>
+<div class="block">Base interface for distributions on the reals.</div>
+<dl><dt><span class="strong">Since:</span></dt>
+ <dd>3.0</dd></dl>
+</li>
+</ul>
+</div>
+<div class="summary">
+<ul class="blockList">
+<li class="blockList">
+<!-- ========== METHOD SUMMARY =========== -->
+<ul class="blockList">
+<li class="blockList"><a name="method_summary">
+<!-- -->
+</a>
+<h3>Method Summary</h3>
+<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
+<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/RealDistribution.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/RealDistribution.html#cumulativeProbability(double,%20double)">cumulativeProbability</a></strong>(double&nbsp;x0,
+ double&nbsp;x1)</code>
+<div class="block"><strong>Deprecated.</strong>&nbsp;
+<div class="block"><i>As of 3.1. In 4.0, this method will be renamed
+ <code>probability(double x0, double x1)</code>.</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/RealDistribution.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/RealDistribution.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/RealDistribution.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/RealDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code>
+<div class="block">Access the lower 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/RealDistribution.html#getSupportUpperBound()">getSupportUpperBound</a></strong>()</code>
+<div class="block">Access the upper 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/RealDistribution.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="altColor">
+<td class="colFirst"><code>boolean</code></td>
+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.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/RealDistribution.html#isSupportLowerBoundInclusive()">isSupportLowerBoundInclusive</a></strong>()</code>
+<div class="block"><strong>Deprecated.</strong>&nbsp;
+<div class="block"><i>to be removed in 4.0</i></div>
+</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/RealDistribution.html#isSupportUpperBoundInclusive()">isSupportUpperBoundInclusive</a></strong>()</code>
+<div class="block"><strong>Deprecated.</strong>&nbsp;
+<div class="block"><i>to be removed in 4.0</i></div>
+</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/RealDistribution.html#probability(double)">probability</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 = x)</code>.</div>
+</td>
+</tr>
+<tr class="altColor">
+<td class="colFirst"><code>void</code></td>
+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a></strong>(long&nbsp;seed)</code>
+<div class="block">Reseed the random generator used to generate samples.</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/RealDistribution.html#sample()">sample</a></strong>()</code>
+<div class="block">Generate a random value sampled from 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/RealDistribution.html#sample(int)">sample</a></strong>(int&nbsp;sampleSize)</code>
+<div class="block">Generate a random sample from the distribution.</div>
+</td>
+</tr>
+</table>
+</li>
+</ul>
+</li>
+</ul>
+</div>
+<div class="details">
+<ul class="blockList">
+<li class="blockList">
+<!-- ============ METHOD DETAIL ========== -->
+<ul class="blockList">
+<li class="blockList"><a name="method_detail">
+<!-- -->
+</a>
+<h3>Method Detail</h3>
+<a name="probability(double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>probability</h4>
+<pre>double&nbsp;probability(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 = x)</code>. In other
+ words, this method represents the probability mass function (PMF)
+ for the distribution.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PMF is evaluated</dd>
+<dt><span class="strong">Returns:</span></dt><dd>the value of the probability mass function at point <code>x</code></dd></dl>
+</li>
+</ul>
+<a name="density(double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>density</h4>
+<pre>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.</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>
+</ul>
+<a name="cumulativeProbability(double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>cumulativeProbability</h4>
+<pre>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.</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>
+<a name="cumulativeProbability(double, double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>cumulativeProbability</h4>
+<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
+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>As of 3.1. In 4.0, this method will be renamed
+ <code>probability(double x0, double x1)</code>.</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>.</div>
+<dl><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>
+</li>
+</ul>
+<a name="inverseCumulativeProbability(double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>inverseCumulativeProbability</h4>
+<pre>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></div>
+<dl><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>
+</ul>
+<a name="getNumericalMean()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>getNumericalMean</h4>
+<pre>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>
+</li>
+</ul>
+<a name="getNumericalVariance()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>getNumericalVariance</h4>
+<pre>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>
+</li>
+</ul>
+<a name="getSupportLowerBound()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>getSupportLowerBound</h4>
+<pre>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>
+</li>
+</ul>
+<a name="getSupportUpperBound()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>getSupportUpperBound</h4>
+<pre>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>
+</li>
+</ul>
+<a name="isSupportLowerBoundInclusive()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>isSupportLowerBoundInclusive</h4>
+<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
+boolean&nbsp;isSupportLowerBoundInclusive()</pre>
+<div class="block"><span class="strong">Deprecated.</span>&nbsp;<i>to be removed in 4.0</i></div>
+<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>
+</li>
+</ul>
+<a name="isSupportUpperBoundInclusive()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>isSupportUpperBoundInclusive</h4>
+<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a>
+boolean&nbsp;isSupportUpperBoundInclusive()</pre>
+<div class="block"><span class="strong">Deprecated.</span>&nbsp;<i>to be removed in 4.0</i></div>
+<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>
+</ul>
+<a name="isSupportConnected()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>isSupportConnected</h4>
+<pre>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>
+</li>
+</ul>
+<a name="reseedRandomGenerator(long)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>reseedRandomGenerator</h4>
+<pre>void&nbsp;reseedRandomGenerator(long&nbsp;seed)</pre>
+<div class="block">Reseed the random generator used to generate samples.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>seed</code> - the new seed</dd></dl>
+</li>
+</ul>
+<a name="sample()">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>sample</h4>
+<pre>double&nbsp;sample()</pre>
+<div class="block">Generate a random value sampled from this distribution.</div>
+<dl><dt><span class="strong">Returns:</span></dt><dd>a random value.</dd></dl>
+</li>
+</ul>
+<a name="sample(int)">
+<!-- -->
+</a>
+<ul class="blockListLast">
+<li class="blockList">
+<h4>sample</h4>
+<pre>double[]&nbsp;sample(int&nbsp;sampleSize)</pre>
+<div class="block">Generate a random sample from the distribution.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>sampleSize</code> - the number of random values to generate</dd>
+<dt><span class="strong">Returns:</span></dt><dd>an array representing the random sample</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>sampleSize</code> is not positive</dd></dl>
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