org.apache.commons.math.distribution
Class PoissonDistributionImpl

java.lang.Object
  org.apache.commons.math.distribution.AbstractDistribution
      org.apache.commons.math.distribution.AbstractIntegerDistribution
          org.apache.commons.math.distribution.PoissonDistributionImpl

All Implemented Interfaces:

java.io.Serializable, DiscreteDistribution, Distribution, IntegerDistribution, PoissonDistribution

public class PoissonDistributionImpl
extends AbstractIntegerDistribution
implements PoissonDistribution, java.io.Serializable

Implementation for the PoissonDistribution.

Version:

$Id: PoissonDistributionImpl.java 1178295 2011-10-03 04:36:27Z psteitz $

See Also:

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.math.distribution.AbstractIntegerDistribution

randomData

Constructor Summary

PoissonDistributionImpl(double p)
Create a new Poisson distribution with the given the mean.

PoissonDistributionImpl(double p, double epsilon)
Create a new Poisson distribution with the given mean and convergence criterion.

PoissonDistributionImpl(double p, double epsilon, int maxIterations)
Create a new Poisson distribution with the given mean, convergence criterion and maximum number of iterations.

PoissonDistributionImpl(double p, int maxIterations)
Create a new Poisson distribution with the given mean and maximum number of iterations.

Method Summary

protected double	calculateNumericalMean() Use this method to actually calculate the mean for the specific distribution.
protected double	calculateNumericalVariance() Use this method to actually calculate the variance for the specific distribution.
double	cumulativeProbability(int x) The probability distribution function P(X <= x) for a Poisson distribution.
protected int	getDomainLowerBound(double p) Access the domain value lower bound, based on p, used to bracket a CDF root.
protected int	getDomainUpperBound(double p) Access the domain value upper bound, based on p, used to bracket a CDF root.
double	getMean() Get the mean for the distribution.
int	getSupportLowerBound() Access the lower bound of the support.
int	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportUpperBoundInclusive() Use this method to get information about whether the upper bound of the support is inclusive or not.
double	normalApproximateProbability(int x) Calculates the Poisson distribution function using a normal approximation.
double	probability(int x) The probability mass function P(X = x) for a Poisson distribution.
int	sample() Generates a random value sampled from this distribution.

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

cumulativeProbability, cumulativeProbability, cumulativeProbability, inverseCumulativeProbability, isSupportLowerBoundInclusive, probability, reseedRandomGenerator, sample

Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

getNumericalMean, getNumericalVariance, isSupportConnected

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math.distribution.IntegerDistribution

cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample

Methods inherited from interface org.apache.commons.math.distribution.DiscreteDistribution

probability

Methods inherited from interface org.apache.commons.math.distribution.Distribution

cumulativeProbability, cumulativeProbability, getNumericalMean, getNumericalVariance, isSupportConnected, isSupportLowerBoundInclusive

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

PoissonDistributionImpl

public PoissonDistributionImpl(double p)

Create a new Poisson distribution with the given the mean. The mean value must be positive; otherwise an IllegalArgument is thrown.

Parameters:

p - the Poisson mean

Throws:

NotStrictlyPositiveException - if p <= 0.

PoissonDistributionImpl

public PoissonDistributionImpl(double p,
                               double epsilon,
                               int maxIterations)

Create a new Poisson distribution with the given 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.

Since:

2.1

PoissonDistributionImpl

public PoissonDistributionImpl(double p,
                               double epsilon)

Create a new Poisson distribution with the given mean and convergence criterion.

Parameters:

p - Poisson mean.

epsilon - Convergence criterion for cumulative probabilities.

Since:

2.1

PoissonDistributionImpl

public PoissonDistributionImpl(double p,
                               int maxIterations)

Create a new Poisson distribution with the given 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.

Specified by:

getMean in interface PoissonDistribution

Returns:

the mean for the distribution.

probability

public double probability(int x)

The probability mass function P(X = x) for a Poisson distribution.

Specified by:

probability in interface IntegerDistribution

Parameters:

x - Value at which the probability density function is evaluated.

Returns:

the value of the probability mass function at x.

cumulativeProbability

public double cumulativeProbability(int x)

The probability distribution function P(X <= x) for a Poisson distribution.

Specified by:

cumulativeProbability in interface IntegerDistribution

Specified by:

cumulativeProbability in class AbstractIntegerDistribution

Parameters:

x - Value at which the PDF is evaluated.

Returns:

the Poisson distribution function evaluated at x. due to convergence or other numerical errors.

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).

Specified by:

normalApproximateProbability in interface PoissonDistribution

Parameters:

x - Upper bound, inclusive.

Returns:

the distribution function value calculated using a normal approximation. approximation.

sample

public int sample()

Generates a random value sampled from this distribution.
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

getDomainLowerBound

protected int getDomainLowerBound(double p)

Access the domain value lower bound, based on p, used to bracket a CDF root. This method is used by AbstractIntegerDistribution.inverseCumulativeProbability(double) to find critical values.

Specified by:

getDomainLowerBound in class AbstractIntegerDistribution

Parameters:

p - Desired probability for the critical value.

Returns:

the domain lower bound.

getDomainUpperBound

protected int getDomainUpperBound(double p)

Access the domain value upper bound, based on p, used to bracket a CDF root. This method is used by AbstractIntegerDistribution.inverseCumulativeProbability(double) to find critical values.

Specified by:

getDomainUpperBound in class AbstractIntegerDistribution

Parameters:

p - Desired probability for the critical value.

Returns:

the domain upper bound.

getSupportLowerBound

public int getSupportLowerBound()

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

Specified by:

getSupportLowerBound in class AbstractIntegerDistribution

Returns:

lower bound of the support (always 0)

getSupportUpperBound

public int getSupportUpperBound()

Access the upper bound of the support. 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 and isSupportUpperBoundInclusive() returns true.

Specified by:

getSupportUpperBound in class AbstractIntegerDistribution

Returns:

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

calculateNumericalMean

protected double calculateNumericalMean()

Use this method to actually calculate the mean for the specific distribution. Use AbstractDistribution.getNumericalMean() (which implements caching) to actually get the mean. For mean parameter p, the mean is p

Specified by:

calculateNumericalMean in class AbstractDistribution

Returns:

the mean or Double.NaN if it's not defined

calculateNumericalVariance

protected double calculateNumericalVariance()

Use this method to actually calculate the variance for the specific distribution. Use AbstractDistribution.getNumericalVariance() (which implements caching) to actually get the variance. For mean parameter p, the variance is p

Specified by:

calculateNumericalVariance in class AbstractDistribution

Returns:

the variance or Double.NaN if it's not defined

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Use this method to get information about whether the upper bound of the support is inclusive or not. For discrete support, only true here is meaningful.

Specified by:

isSupportUpperBoundInclusive in interface Distribution

Overrides:

isSupportUpperBoundInclusive in class AbstractIntegerDistribution

Returns:

true (always but at Integer.MAX_VALUE because of the nature of discrete support)