cern.jet.random

Class Gamma

java.lang.Object

cern.colt.PersistentObject

cern.jet.random.AbstractDistribution

cern.jet.random.AbstractContinousDistribution

cern.jet.random.Gamma

All Implemented Interfaces:

DoubleFunction, IntFunction, Serializable, Cloneable

public class Gamma
extends AbstractContinousDistribution

Gamma distribution; math definition, definition of gamma function and animated definition.

p(x) = k * x^(alpha-1) * e^(-x/beta) with k = 1/(g(alpha) * b^a)) and g(a) being the gamma function.

Valid parameter ranges: alpha > 0.

Note: For a Gamma distribution to have the mean mean and variance variance, set the parameters as follows:

 alpha = mean*mean / variance; lambda = 1 / (variance / mean); 
 

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation:

Method: Acceptance Rejection combined with Acceptance Complement.

High performance implementation. This is a port of RandGamma used in CLHEP 1.4.0 (C++). CLHEP's implementation, in turn, is based on gds.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

J.H. Ahrens, U. Dieter (1974): Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing 12, 223-246.

and

J.H. Ahrens, U. Dieter (1982): Generating gamma variates by a modified rejection technique, Communications of the ACM 25, 47-54.

Version:

1.0, 09/24/99

Author:

wolfgang.hoschek@cern.ch

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected double	alpha
protected double	lambda
protected static Gamma	shared

Fields inherited from class cern.jet.random.AbstractDistribution

randomGenerator

Fields inherited from class cern.colt.PersistentObject

serialVersionUID

Constructor Summary

Constructors

Constructor and Description
Gamma(double alpha, double lambda, RandomEngine randomGenerator) Constructs a Gamma distribution.

Method Summary

Methods

Modifier and Type	Method and Description
double	cdf(double x) Returns the cumulative distribution function.
double	nextDouble() Returns a random number from the distribution.
double	nextDouble(double alpha, double lambda) Returns a random number from the distribution; bypasses the internal state.
double	pdf(double x) Returns the probability distribution function.
void	setState(double alpha, double lambda) Sets the mean and variance.
static double	staticNextDouble(double alpha, double lambda) Returns a random number from the distribution.
String	toString() Returns a String representation of the receiver.

Methods inherited from class cern.jet.random.AbstractDistribution

apply, apply, clone, getRandomGenerator, makeDefaultGenerator, nextInt, setRandomGenerator

Methods inherited from class java.lang.Object

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

Field Detail

alpha

protected double alpha

lambda

protected double lambda

shared

protected static Gamma shared

Constructor Detail

Gamma

public Gamma(double alpha,
     double lambda,
     RandomEngine randomGenerator)

Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.

Throws:

IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.

Method Detail

cdf

public double cdf(double x)

Returns the cumulative distribution function.

nextDouble

public double nextDouble()

Returns a random number from the distribution.

Specified by:

nextDouble in class AbstractDistribution

nextDouble

public double nextDouble(double alpha,
                double lambda)

Returns a random number from the distribution; bypasses the internal state.

pdf

public double pdf(double x)

Returns the probability distribution function.

setState

public void setState(double alpha,
            double lambda)

Sets the mean and variance.

Throws:

IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.

staticNextDouble

public static double staticNextDouble(double alpha,
                      double lambda)

Returns a random number from the distribution.

Throws:

IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.

toString

public String toString()

Returns a String representation of the receiver.

Overrides:

toString in class Object