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<h2 title="Class BetaDistribution" class="title">Class BetaDistribution</h2>
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<pre>public class <span class="strong">BetaDistribution</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">Implements the Beta distribution.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0 (changed to concrete class in 3.0)</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Beta_distribution">Beta distribution</a>,
<a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.BetaDistribution">Serialized Form</a></dd></dl>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.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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<h3>Fields inherited from class org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></h3>
<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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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#BetaDistribution(double,%20double)">BetaDistribution</a></strong>(double alpha,
double beta)</code>
<div class="block">Build a new instance.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#BetaDistribution(double,%20double,%20double)">BetaDistribution</a></strong>(double alpha,
double beta,
double inverseCumAccuracy)</code>
<div class="block">Build a new instance.</div>
</td>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#BetaDistribution(org.apache.commons.math3.random.RandomGenerator,%20double,%20double)">BetaDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double alpha,
double beta)</code>
<div class="block">Creates a β distribution.</div>
</td>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#BetaDistribution(org.apache.commons.math3.random.RandomGenerator,%20double,%20double,%20double)">BetaDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double alpha,
double beta,
double inverseCumAccuracy)</code>
<div class="block">Creates a β distribution.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#cumulativeProbability(double)">cumulativeProbability</a></strong>(double 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>
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<tr class="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#density(double)">density</a></strong>(double x)</code>
<div class="block">Returns the probability density function (PDF) of this distribution
evaluated at the specified point <code>x</code>.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#getAlpha()">getAlpha</a></strong>()</code>
<div class="block">Access the first shape parameter, <code>alpha</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/BetaDistribution.html#getBeta()">getBeta</a></strong>()</code>
<div class="block">Access the second shape parameter, <code>beta</code>.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.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>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.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>
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<td class="colFirst"><code>protected double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</a></strong>()</code>
<div class="block">Return the absolute accuracy setting of the solver used to estimate
inverse cumulative probabilities.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code>
<div class="block">Access the lower bound of the support.</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#getSupportUpperBound()">getSupportUpperBound</a></strong>()</code>
<div class="block">Access the upper bound of the support.</div>
</td>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.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/BetaDistribution.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>
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<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.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>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#logDensity(double)">logDensity</a></strong>(double 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>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#sample()">sample</a></strong>()</code>
<div class="block">Generate a random value sampled from this distribution.</div>
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<h3>Methods inherited from class org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></h3>
<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#cumulativeProbability(double,%20double)">cumulativeProbability</a>, <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#probability(double,%20double)">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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<h4>DEFAULT_INVERSE_ABSOLUTE_ACCURACY</h4>
<pre>public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY</pre>
<div class="block">Default inverse cumulative probability accuracy.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.distribution.BetaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY">Constant Field Values</a></dd></dl>
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<pre>public BetaDistribution(double alpha,
double beta)</pre>
<div class="block">Build a new instance.
<p>
<b>Note:</b> this constructor will implicitly create an instance of
<a href="../../../../../org/apache/commons/math3/random/Well19937c.html" title="class in org.apache.commons.math3.random"><code>Well19937c</code></a> as random generator to be used for sampling only (see
<a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#sample()"><code>sample()</code></a> and <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample(int)"><code>AbstractRealDistribution.sample(int)</code></a>). In case no sampling is
needed for the created distribution, it is advised to pass <code>null</code>
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>alpha</code> - First shape parameter (must be positive).</dd><dd><code>beta</code> - Second shape parameter (must be positive).</dd></dl>
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<pre>public BetaDistribution(double alpha,
double beta,
double inverseCumAccuracy)</pre>
<div class="block">Build a new instance.
<p>
<b>Note:</b> this constructor will implicitly create an instance of
<a href="../../../../../org/apache/commons/math3/random/Well19937c.html" title="class in org.apache.commons.math3.random"><code>Well19937c</code></a> as random generator to be used for sampling only (see
<a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#sample()"><code>sample()</code></a> and <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample(int)"><code>AbstractRealDistribution.sample(int)</code></a>). In case no sampling is
needed for the created distribution, it is advised to pass <code>null</code>
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>alpha</code> - First shape parameter (must be positive).</dd><dd><code>beta</code> - Second shape parameter (must be positive).</dd><dd><code>inverseCumAccuracy</code> - Maximum absolute error in inverse
cumulative probability estimates (defaults to
<a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#DEFAULT_INVERSE_ABSOLUTE_ACCURACY"><code>DEFAULT_INVERSE_ABSOLUTE_ACCURACY</code></a>).</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
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<pre>public BetaDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double alpha,
double beta)</pre>
<div class="block">Creates a β distribution.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>alpha</code> - First shape parameter (must be positive).</dd><dd><code>beta</code> - Second shape parameter (must be positive).</dd><dt><span class="strong">Since:</span></dt>
<dd>3.3</dd></dl>
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<pre>public BetaDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double alpha,
double beta,
double inverseCumAccuracy)</pre>
<div class="block">Creates a β distribution.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>alpha</code> - First shape parameter (must be positive).</dd><dd><code>beta</code> - Second shape parameter (must be positive).</dd><dd><code>inverseCumAccuracy</code> - Maximum absolute error in inverse
cumulative probability estimates (defaults to
<a href="../../../../../org/apache/commons/math3/distribution/BetaDistribution.html#DEFAULT_INVERSE_ABSOLUTE_ACCURACY"><code>DEFAULT_INVERSE_ABSOLUTE_ACCURACY</code></a>).</dd><dt><span class="strong">Since:</span></dt>
<dd>3.1</dd></dl>
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<h4>getAlpha</h4>
<pre>public double getAlpha()</pre>
<div class="block">Access the first shape parameter, <code>alpha</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the first shape parameter.</dd></dl>
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<pre>public double getBeta()</pre>
<div class="block">Access the second shape parameter, <code>beta</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the second shape parameter.</dd></dl>
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<pre>public double density(double 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>
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<pre>public double logDensity(double 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>.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#logDensity(double)">logDensity</a></code> in class <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 double cumulativeProbability(double 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 (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>
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<pre>protected double getSolverAbsoluteAccuracy()</pre>
<div class="block">Return the absolute accuracy setting of the solver used to estimate
inverse cumulative probabilities.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</a></code> in class <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 solver absolute accuracy.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
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<pre>public double getNumericalMean()</pre>
<div class="block">Use this method to get the numerical value of the mean of this
distribution.
For first shape parameter <code>alpha</code> and second shape parameter
<code>beta</code>, the mean is <code>alpha / (alpha + beta)</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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<pre>public double getNumericalVariance()</pre>
<div class="block">Use this method to get the numerical value of the variance of this
distribution.
For first shape parameter <code>alpha</code> and second shape parameter
<code>beta</code>, the variance is
<code>(alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)]</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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<pre>public double 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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<pre>public double 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 1 no matter the parameters.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support (always 1)</dd></dl>
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<pre>public boolean 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 boolean 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 boolean 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>
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<h4>sample</h4>
<pre>public double 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>
<p>
Sampling is performed using Cheng algorithms:
</p>
<p>
R. C. H. Cheng, "Generating beta variates with nonintegral shape parameters.".
Communications of the ACM, 21, 317–322, 1978.
</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#sample()">sample</a></code> in interface <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> in class <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>
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