edu.uah.math.distributions

Class GammaDistribution

java.lang.Object

edu.uah.math.distributions.Distribution

edu.uah.math.distributions.GammaDistribution

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

ChiSquareDistribution, ExponentialDistribution

public class GammaDistribution
extends Distribution
implements java.io.Serializable

This class models the gamma distribution with a specified shape parameter and scale parameter. This distribution governs the time of an event in the Poisson process.

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

Constructors

Constructor and Description
GammaDistribution() This default constructor creates a new gamma distribution with shape parameter 1 and scale parameter 1.
GammaDistribution(double k, double b) This general constructor creates a new gamma distribution with specified shape parameter and scale parameters.

Method Summary

Methods

Modifier and Type	Method and Description
double	getCDF(double x) This method computes the cumulative distribution function of the distribution.
double	getDensity(double x) This method computes the probability density function,
double	getMaxDensity() This method returns the maximum value of the density function.
double	getMean() This method returns the mean bk.
double	getMGF(double t) This method returns the moment generating function.
double	getMoment(double a, int n) This method returns the moment a specified order about a specified point.
double	getMoment(int n) This method returns the moment of order n.
double	getScale() This method returns the scale parameter.
double	getShape() This method returns the shape parameter.
double	getVariance() This method returns the variance kb2.
void	setParameters(double k, double b) This method sets the parameters and creates the default domain.
void	setScale(double b) This method sets the scale parameters.
void	setShape(double k) This method sets the shape parameter.
double	simulate() This method simulates a value from the distribution.
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, getPGF, getQuantile, getSD, getType, setDomain, setDomain

Methods inherited from class java.lang.Object

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

Constructor Detail

GammaDistribution

public GammaDistribution(double k,
                 double b)

This general constructor creates a new gamma distribution with specified shape parameter and scale parameters.

Parameters:

k - the shape parameter

b - the scale parameter

GammaDistribution

public GammaDistribution()

This default constructor creates a new gamma distribution with shape parameter 1 and scale parameter 1.

Method Detail

setParameters

public void setParameters(double k,
                 double b)

This method sets the parameters and creates the default domain.

Parameters:

k - the shape parameter

b - the scale parameter

setShape

public void setShape(double k)

This method sets the shape parameter.

Parameters:

k - the shape parameter

getShape

public double getShape()

This method returns the shape parameter.

Returns:

the shape parameter

setScale

public void setScale(double b)

This method sets the scale parameters.

Parameters:

b - the scale parameter

getScale

public double getScale()

This method returns the scale parameter.

Returns:

the scale parameter

getDensity

public double getDensity(double x)

This method computes the probability density function,

Specified by:

getDensity in class Distribution

Parameters:

x - a number > 0

Returns:

the probability density at x

getMaxDensity

public double getMaxDensity()

This method returns the maximum value of the density function. If the shape parameter is < 1, the maximum value is ∞ at x = 0. If the shape parameter is ≥ 1, the maximum occurs at x = b(k &minus 1).

Overrides:

getMaxDensity in class Distribution

Returns:

the maximum value of the probability density function

getMean

public double getMean()

This method returns the mean bk.

Overrides:

getMean in class Distribution

Returns:

the mean of the distribution

getVariance

public double getVariance()

This method returns the variance kb².

Overrides:

getVariance in class Distribution

Returns:

the variance of the distribution

getMoment

public double getMoment(int n)

This method returns the moment of order n.

Overrides:

getMoment in class Distribution

Parameters:

n - the order

Returns:

the moment of order n

getMoment

public double getMoment(double a,
               int n)

This method returns the moment a specified order about a specified point.

Overrides:

getMoment in class Distribution

Parameters:

a - the center

n - the order

Returns:

the moment of order n about a

getMGF

public double getMGF(double t)

This method returns the moment generating function. This function is given by M(t) = (1 &minus bt)^−k for t < 1/b.

Overrides:

getMGF in class Distribution

Parameters:

t - a number in the domain of the MGF

Returns:

the moment generating function at t

getCDF

public double getCDF(double x)

This method computes the cumulative distribution function of the distribution.

Overrides:

getCDF in class Distribution

Parameters:

x - a number in the domain of the distribution

Returns:

the cumulative probability at x

simulate

public double simulate()

This method simulates a value from the distribution. If shape parameter is an integer, this is done by simulating an arrival time in a Poisson proccess.

Overrides:

simulate in class Distribution

Returns:

a simulated value from 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