cern.jet.stat

Class Gamma

java.lang.Object

cern.jet.math.Constants

cern.jet.stat.Gamma

public class Gamma
extends Constants

Gamma and Beta functions.

Implementation:

Some code taken and adapted from the Java 2D Graph Package 2.4, which in turn is a port from the Cephes 2.2 Math Library (C). Most Cephes code (missing from the 2D Graph Package) directly ported.

Version:

0.9, 22-Jun-99

Author:

wolfgang.hoschek@cern.ch

Field Summary

Fields inherited from class cern.jet.math.Constants

big, biginv, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	Gamma() Makes this class non instantiable, but still let's others inherit from it.

Method Summary

Methods

Modifier and Type	Method and Description
static double	beta(double a, double b) Returns the beta function of the arguments.
static double	gamma(double x) Returns the Gamma function of the argument.
static double	incompleteBeta(double aa, double bb, double xx) Returns the Incomplete Beta Function evaluated from zero to xx; formerly named ibeta.
static double	incompleteGamma(double a, double x) Returns the Incomplete Gamma function; formerly named igamma.
static double	incompleteGammaComplement(double a, double x) Returns the Complemented Incomplete Gamma function; formerly named igamc.
static double	logGamma(double x) Returns the natural logarithm of the gamma function; formerly named lgamma.

Methods inherited from class java.lang.Object

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

Constructor Detail

Gamma

protected Gamma()

Makes this class non instantiable, but still let's others inherit from it.

Method Detail

beta

public static double beta(double a,
          double b)
                   throws ArithmeticException

Returns the beta function of the arguments.

                   -     -
                  | (a) | (b)
 beta( a, b )  =  -----------.
                     -
                    | (a+b)
 

Throws:

ArithmeticException

gamma

public static double gamma(double x)
                    throws ArithmeticException

Returns the Gamma function of the argument.

Throws:

ArithmeticException

incompleteBeta

public static double incompleteBeta(double aa,
                    double bb,
                    double xx)
                             throws ArithmeticException

Returns the Incomplete Beta Function evaluated from zero to xx; formerly named ibeta.

Parameters:

aa - the alpha parameter of the beta distribution.

bb - the beta parameter of the beta distribution.

xx - the integration end point.

Throws:

ArithmeticException

incompleteGamma

public static double incompleteGamma(double a,
                     double x)
                              throws ArithmeticException

Returns the Incomplete Gamma function; formerly named igamma.

Parameters:

a - the parameter of the gamma distribution.

x - the integration end point.

Throws:

ArithmeticException

incompleteGammaComplement

public static double incompleteGammaComplement(double a,
                               double x)
                                        throws ArithmeticException

Returns the Complemented Incomplete Gamma function; formerly named igamc.

Parameters:

a - the parameter of the gamma distribution.

x - the integration start point.

Throws:

ArithmeticException

logGamma

public static double logGamma(double x)
                       throws ArithmeticException

Returns the natural logarithm of the gamma function; formerly named lgamma.

Throws:

ArithmeticException