edu.uah.math.distributions
Class PoissonDistribution

java.lang.Object
  edu.uah.math.distributions.Distribution
      edu.uah.math.distributions.PoissonDistribution

All Implemented Interfaces:

java.io.Serializable

public class PoissonDistribution
extends Distribution
implements java.io.Serializable

The class models the Poisson distribution with a specified rate parameter.

Version:

August, 2003

Author:

Kyle Siegrist, Dawn Duehring

See Also:

Serialized Form

Field Summary

Fields inherited from class edu.uah.math.distributions.Distribution

CONTINUOUS, DISCRETE, MIXED

Constructor Summary

PoissonDistribution()
This default constructor creates a new Poisson distribtiton with parameter 1.

PoissonDistribution(double r)
This default constructor creates a new Poisson distribution with a given parameter value.

Method Summary

double	getCDF(double x) This method computes the cumulative distribution function in terms of the gamma cumulative distribution function.
double	getDensity(double x) This method computes the probability density function.
double	getFactorialMoment(int n) This method returns the factorial moment of a specified order.
double	getMaxDensity() This method returns the maximum value of the density function.
double	getMean() This method returns the mean of the distribution.
double	getMGF(double t) This method returns the moment generating function.
double	getParameter() This method sets the rate parameter.
double	getPGF(double t) This method returns the probability generating function.
double	getVariance() This method returns the variance of the distribution.
void	setParameter(double r) This method sets the parameter and creates the domain of the distribution.
double	simulate() This method simulates a value from the distribution, by simulating the number of arrivals in an interval of parameter length in a Poisson process with rate 1.
java.lang.String	toString() This method returns a string that gives the name of the distribution and the values of the parameters.

Methods inherited from class edu.uah.math.distributions.Distribution

getDomain, getFailureRate, getMedian, getMoment, getMoment, getQuantile, getSD, getType, setDomain, setDomain

Methods inherited from class java.lang.Object

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

Constructor Detail

PoissonDistribution

public PoissonDistribution(double r)

This default constructor creates a new Poisson distribution with a given parameter value.

Parameters:

r - the rate parameter

PoissonDistribution

public PoissonDistribution()

This default constructor creates a new Poisson distribtiton with parameter 1.

Method Detail

setParameter

public void setParameter(double r)

This method sets the parameter and creates the domain of the distribution.

Parameters:

r - the rate parameter

getParameter

public double getParameter()

This method sets the rate parameter.

Returns:

the rate parameter

getDensity

public double getDensity(double x)

This method computes the probability density function.

Specified by:

getDensity in class Distribution

Parameters:

x - a number in the domain of the distribution

Returns:

the probability density at x

getMaxDensity

public double getMaxDensity()

This method returns the maximum value of the density function.

Overrides:

getMaxDensity in class Distribution

Returns:

the maximum value of the probability density function

getCDF

public double getCDF(double x)

This method computes the cumulative distribution function in terms of the gamma cumulative distribution function.

Overrides:

getCDF in class Distribution

Parameters:

x - a number in the domain of the distribution

Returns:

the cumulative probability at x

getMean

public double getMean()

This method returns the mean of the distribution.

Overrides:

getMean in class Distribution

Returns:

the mean

getVariance

public double getVariance()

This method returns the variance of the distribution.

Overrides:

getVariance in class Distribution

Returns:

the variance

getFactorialMoment

public double getFactorialMoment(int n)

This method returns the factorial moment of a specified order.

Parameters:

n - the order

Returns:

the facotrial moment

getPGF

public double getPGF(double t)

This method returns the probability generating function.

Overrides:

getPGF in class Distribution

Parameters:

t - a real number

Returns:

the probability generating function at t

getMGF

public double getMGF(double t)

This method returns the moment generating function.

Overrides:

getMGF in class Distribution

Parameters:

t - a real number

Returns:

the moment generating function at t

simulate

public double simulate()

This method simulates a value from the distribution, by simulating the number of arrivals in an interval of parameter length in a Poisson process with rate 1.

Overrides:

simulate in class Distribution

Returns:

a simulated value form the distribution

toString

public java.lang.String toString()

This method returns a string that gives the name of the distribution and the values of the parameters.

Overrides:

toString in class Distribution

Returns:

a string giving the name of the distribution and the values of the parameters