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

Methods
`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`