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<h2 title="Class PoissonDistribution" class="title">Class PoissonDistribution</h2>
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<pre>public class <span class="strong">PoissonDistribution</span>
extends <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></pre>
<div class="block">Implementation of the Poisson distribution.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution (Wikipedia)</a>,
<a href="http://mathworld.wolfram.com/PoissonDistribution.html">Poisson distribution (MathWorld)</a>,
<a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.PoissonDistribution">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/PoissonDistribution.html#DEFAULT_EPSILON">DEFAULT_EPSILON</a></strong></code>
<div class="block">Default convergence criterion.</div>
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<td class="colFirst"><code>static int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#DEFAULT_MAX_ITERATIONS">DEFAULT_MAX_ITERATIONS</a></strong></code>
<div class="block">Default maximum number of iterations for cumulative probability calculations.</div>
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<h3>Fields inherited from class org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></h3>
<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#random">random</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#randomData">randomData</a></code></li>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#PoissonDistribution(double)">PoissonDistribution</a></strong>(double p)</code>
<div class="block">Creates a new Poisson distribution with specified mean.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#PoissonDistribution(double,%20double)">PoissonDistribution</a></strong>(double p,
double epsilon)</code>
<div class="block">Creates a new Poisson distribution with the specified mean and
convergence criterion.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#PoissonDistribution(double,%20double,%20int)">PoissonDistribution</a></strong>(double p,
double epsilon,
int maxIterations)</code>
<div class="block">Creates a new Poisson distribution with specified mean, convergence
criterion and maximum number of iterations.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#PoissonDistribution(double,%20int)">PoissonDistribution</a></strong>(double p,
int maxIterations)</code>
<div class="block">Creates a new Poisson distribution with the specified mean and maximum
number of iterations.</div>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#PoissonDistribution(org.apache.commons.math3.random.RandomGenerator,%20double,%20double,%20int)">PoissonDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double p,
double epsilon,
int maxIterations)</code>
<div class="block">Creates a new Poisson distribution with specified mean, convergence
criterion and maximum number of iterations.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#cumulativeProbability(int)">cumulativeProbability</a></strong>(int 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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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#getMean()">getMean</a></strong>()</code>
<div class="block">Get the mean for the 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/PoissonDistribution.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/PoissonDistribution.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>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code>
<div class="block">Access the lower bound of the support.</div>
</td>
</tr>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.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/PoissonDistribution.html#isSupportConnected()">isSupportConnected</a></strong>()</code>
<div class="block">Use this method to get information about whether the support is
connected, i.e.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#logProbability(int)">logProbability</a></strong>(int x)</code>
<div class="block">For a random variable <code>X</code> whose values are distributed according to
this distribution, this method returns <code>log(P(X = x))</code>, where
<code>log</code> is the natural logarithm.</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/PoissonDistribution.html#normalApproximateProbability(int)">normalApproximateProbability</a></strong>(int x)</code>
<div class="block">Calculates the Poisson distribution function using a normal
approximation.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.html#probability(int)">probability</a></strong>(int 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>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/PoissonDistribution.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/AbstractIntegerDistribution.html#cumulativeProbability(int,%20int)">cumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample(int)">sample</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#solveInverseCumulativeProbability(double,%20int,%20int)">solveInverseCumulativeProbability</a></code></li>
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<h4>DEFAULT_MAX_ITERATIONS</h4>
<pre>public static final int DEFAULT_MAX_ITERATIONS</pre>
<div class="block">Default maximum number of iterations for cumulative probability calculations.</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.PoissonDistribution.DEFAULT_MAX_ITERATIONS">Constant Field Values</a></dd></dl>
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<pre>public static final double DEFAULT_EPSILON</pre>
<div class="block">Default convergence criterion.</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.PoissonDistribution.DEFAULT_EPSILON">Constant Field Values</a></dd></dl>
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<pre>public PoissonDistribution(double p)
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 new Poisson distribution with specified mean.
<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/PoissonDistribution.html#sample()"><code>sample()</code></a> and <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample(int)"><code>AbstractIntegerDistribution.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>p</code> - the Poisson mean</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>p <= 0</code>.</dd></dl>
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<pre>public PoissonDistribution(double p,
double epsilon,
int maxIterations)
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 new Poisson distribution with specified mean, convergence
criterion and maximum number of iterations.
<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/PoissonDistribution.html#sample()"><code>sample()</code></a> and <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample(int)"><code>AbstractIntegerDistribution.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>p</code> - Poisson mean.</dd><dd><code>epsilon</code> - Convergence criterion for cumulative probabilities.</dd><dd><code>maxIterations</code> - the maximum number of iterations for cumulative
probabilities.</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>p <= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
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<pre>public PoissonDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng,
double p,
double epsilon,
int maxIterations)
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 new Poisson distribution with specified mean, convergence
criterion and maximum number of iterations.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>p</code> - Poisson mean.</dd><dd><code>epsilon</code> - Convergence criterion for cumulative probabilities.</dd><dd><code>maxIterations</code> - the maximum number of iterations for cumulative
probabilities.</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>p <= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>3.1</dd></dl>
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<pre>public PoissonDistribution(double p,
double epsilon)
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 new Poisson distribution with the specified mean and
convergence criterion.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>p</code> - Poisson mean.</dd><dd><code>epsilon</code> - Convergence criterion for cumulative probabilities.</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>p <= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
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<pre>public PoissonDistribution(double p,
int maxIterations)</pre>
<div class="block">Creates a new Poisson distribution with the specified mean and maximum
number of iterations.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>p</code> - Poisson mean.</dd><dd><code>maxIterations</code> - Maximum number of iterations for cumulative
probabilities.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.1</dd></dl>
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<pre>public double getMean()</pre>
<div class="block">Get the mean for the distribution.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the mean for the distribution.</dd></dl>
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<pre>public double probability(int 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 <code>x</code></dd></dl>
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<pre>public double logProbability(int x)</pre>
<div class="block">For a random variable <code>X</code> whose values are distributed according to
this distribution, this method returns <code>log(P(X = x))</code>, where
<code>log</code> is the natural logarithm. In other words, this method
represents the logarithm of the probability mass function (PMF) for the
distribution. 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/IntegerDistribution.html#probability(int)"><code>IntegerDistribution.probability(int)</code></a>.
<p>
The default implementation simply computes the logarithm of <code>probability(x)</code>.</p></div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#logProbability(int)">logProbability</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></code></dd>
<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 logarithm of the value of the probability mass function at <code>x</code></dd></dl>
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<pre>public double cumulativeProbability(int 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>public double normalApproximateProbability(int x)</pre>
<div class="block">Calculates the Poisson distribution function using a normal
approximation. The <code>N(mean, sqrt(mean))</code> distribution is used
to approximate the Poisson distribution. The computation uses
"half-correction" (evaluating the normal distribution function at
<code>x + 0.5</code>).</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Upper bound, inclusive.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the distribution function value calculated using a normal
approximation.</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 mean parameter <code>p</code>, the mean is <code>p</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 mean parameter <code>p</code>, the variance is <code>p</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the variance (possibly <code>Double.POSITIVE_INFINITY</code> or
<code>Double.NaN</code> if it is not defined)</dd></dl>
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<pre>public int 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 Z | P(X <= x) > 0}</code>.</p>
The lower bound of the support is always 0 no matter the mean parameter.</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 int 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 positive infinity,
regardless of the parameter values. There is no integer infinity,
so this method returns <code>Integer.MAX_VALUE</code>.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support (always <code>Integer.MAX_VALUE</code> for
positive infinity)</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 integers 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 int 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>
<strong>Algorithm Description</strong>:
<ul>
<li>For small means, uses simulation of a Poisson process
using Uniform deviates, as described
<a href="http://mathaa.epfl.ch/cours/PMMI2001/interactive/rng7.htm"> here</a>.
The Poisson process (and hence value returned) is bounded by 1000 * mean.
</li>
<li>For large means, uses the rejection algorithm described in
<blockquote>
Devroye, Luc. (1981).<i>The Computer Generation of Poisson Random Variables</i><br>
<strong>Computing</strong> vol. 26 pp. 197-207.<br>
</blockquote>
</li>
</ul>
</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/IntegerDistribution.html#sample()">sample</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/distribution/IntegerDistribution.html" title="interface in org.apache.commons.math3.distribution">IntegerDistribution</a></code></dd>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample()">sample</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>a random value.</dd><dt><span class="strong">Since:</span></dt>
<dd>2.2</dd></dl>
</li>
</ul>
</li>
</ul>
</li>
</ul>
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