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

Method Summary

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

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

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