org.apache.commons.math3.distribution
Class PoissonDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractIntegerDistribution
      org.apache.commons.math3.distribution.PoissonDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

public class PoissonDistribution
extends AbstractIntegerDistribution

Implementation of the Poisson distribution.

Version:

$Id: PoissonDistribution.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Poisson distribution (Wikipedia), Poisson distribution (MathWorld), Serialized Form

Field Summary

static double	DEFAULT_EPSILON Default convergence criterion.
static int	DEFAULT_MAX_ITERATIONS Default maximum number of iterations for cumulative probability calculations.

Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

random, randomData

Constructor Summary

PoissonDistribution(double p)
Creates a new Poisson distribution with specified mean.

PoissonDistribution(double p, double epsilon)
Creates a new Poisson distribution with the specified mean and convergence criterion.

PoissonDistribution(double p, double epsilon, int maxIterations)
Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.

PoissonDistribution(double p, int maxIterations)
Creates a new Poisson distribution with the specified mean and maximum number of iterations.

PoissonDistribution(RandomGenerator rng, double p, double epsilon, int maxIterations)
Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.

Method Summary

double	cumulativeProbability(int x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	getMean() Get the mean for the distribution.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
int	getSupportLowerBound() Access the lower bound of the support.
int	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
double	normalApproximateProbability(int x) Calculates the Poisson distribution function using a normal approximation.
double	probability(int x) For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
int	sample() Generate a random value sampled from this distribution.

Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, solveInverseCumulativeProbability

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_MAX_ITERATIONS

public static final int DEFAULT_MAX_ITERATIONS

Default maximum number of iterations for cumulative probability calculations.

Since:

2.1

See Also:

Constant Field Values

DEFAULT_EPSILON

public static final double DEFAULT_EPSILON

Default convergence criterion.

Since:

2.1

See Also:

Constant Field Values

Constructor Detail

PoissonDistribution

public PoissonDistribution(double p)
                    throws NotStrictlyPositiveException

Creates a new Poisson distribution with specified mean.

Parameters:

p - the Poisson mean

Throws:

NotStrictlyPositiveException - if p <= 0.

PoissonDistribution

public PoissonDistribution(double p,
                           double epsilon,
                           int maxIterations)
                    throws NotStrictlyPositiveException

Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.

Parameters:

p - Poisson mean.

epsilon - Convergence criterion for cumulative probabilities.

maxIterations - the maximum number of iterations for cumulative probabilities.

Throws:

NotStrictlyPositiveException - if p <= 0.

Since:

2.1

PoissonDistribution

public PoissonDistribution(RandomGenerator rng,
                           double p,
                           double epsilon,
                           int maxIterations)
                    throws NotStrictlyPositiveException

Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.

Parameters:

rng - Random number generator.

p - Poisson mean.

epsilon - Convergence criterion for cumulative probabilities.

maxIterations - the maximum number of iterations for cumulative probabilities.

Throws:

NotStrictlyPositiveException - if p <= 0.

Since:

3.1

PoissonDistribution

public PoissonDistribution(double p,
                           double epsilon)
                    throws NotStrictlyPositiveException

Creates a new Poisson distribution with the specified mean and convergence criterion.

Parameters:

p - Poisson mean.

epsilon - Convergence criterion for cumulative probabilities.

Throws:

NotStrictlyPositiveException - if p <= 0.

Since:

2.1

PoissonDistribution

public PoissonDistribution(double p,
                           int maxIterations)

Creates a new Poisson distribution with the specified mean and maximum number of iterations.

Parameters:

p - Poisson mean.

maxIterations - Maximum number of iterations for cumulative probabilities.

Since:

2.1

Method Detail

getMean

public double getMean()

Get the mean for the distribution.

Returns:

the mean for the distribution.

probability

public double probability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at x

cumulativeProbability

public double cumulativeProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

normalApproximateProbability

public double normalApproximateProbability(int x)

Calculates the Poisson distribution function using a normal approximation. The N(mean, sqrt(mean)) distribution is used to approximate the Poisson distribution. The computation uses "half-correction" (evaluating the normal distribution function at x + 0.5).

Parameters:

x - Upper bound, inclusive.

Returns:

the distribution function value calculated using a normal approximation.

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For mean parameter p, the mean is p.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For mean parameter p, the variance is p.

Returns:

the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)

getSupportLowerBound

public int getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in Z | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the mean parameter.

Returns:

lower bound of the support (always 0)

getSupportUpperBound

public int getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is positive infinity, regardless of the parameter values. There is no integer infinity, so this method returns Integer.MAX_VALUE.

Returns:

upper bound of the support (always Integer.MAX_VALUE for positive infinity)

isSupportConnected

public boolean isSupportConnected()

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.

Returns:

true

sample

public int sample()

Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Algorithm Description:

• For small means, uses simulation of a Poisson process using Uniform deviates, as described here. The Poisson process (and hence value returned) is bounded by 1000 * mean.
• For large means, uses the rejection algorithm described in Devroye, Luc. (1981).The Computer Generation of Poisson Random Variables Computing vol. 26 pp. 197-207.

Specified by:

sample in interface IntegerDistribution

Overrides:

sample in class AbstractIntegerDistribution

Returns:

a random value.

Since:

2.2