papaya
Class Gamma

java.lang.Object
  papaya.Gamma

All Implemented Interfaces:

PapayaConstants

public class Gamma
extends Object
implements PapayaConstants

Gamma and Beta functions.

Implementation: The code is mostly adapted from the CERN Jet Java libraries, which in turn was adapted from the Cephes Mathematical Library. As far a as I can tell, Stephen L. Moshier wrote the original C++ code for CEPHES (1989, moshier@na-net.ornl.gov) and Wolfgang Hoschek (at CERN, hats off to you mate!) then adapted it for the Java platform, making some significant changes along the way.

Field Summary

Fields inherited from interface papaya.PapayaConstants

BASELINE, big, biginv, BOTTOM, CENTER, CORNER, FONTNAME, GRAY, INDEX_NOT_FOUND, INDICES_NOT_FOUND, LEFT, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, RIGHT, SQRTH, SQTPI, STROKEWEIGHT, TEXTSIZE, TOP

Method Summary

static float	beta(double a, double b) Returns the beta function of the arguments.
static double	gamma(double x) Returns the Gamma function of the argument, Γ(x)
static double	incompleteBeta(double aa, double bb, double xx) Returns the Incomplete Beta Function evaluated from zero to xx; formerly named ibeta.
static double	incompleteBetaInverse(double aa, double bb, double yy0) Returns the inverse of the incomplete Beta integral.
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 float beta(double a,
                         double b)
                  throws ArithmeticException

Returns the beta function of the arguments.

 
 beta( a, b )  = Γ(a) * Γ(b) ) Γ(a+b)

 

Throws:

ArithmeticException

gamma

public static double gamma(double x)
                    throws ArithmeticException

Returns the Gamma function of the argument, Γ(x)

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

incompleteBetaInverse

public static double incompleteBetaInverse(double aa,
                                           double bb,
                                           double yy0)

Returns the inverse of the incomplete Beta integral. That is, given y, the function finds x such that

  incompleteBeta( a, b, x ) = y.

The routine performs interval halving until incompleteBeta(a,b,x) - y = 0, to within roughly 10^-13 of the true solution. If this precision is not reached, the method returns the current approximation of x, and prints a warning statement specifying the current error. Typically, this is on the order of 10^-12.

Parameters:

aa - the alpha parameter of the beta distribution.

bb - the beta parameter of the beta distribution.

yy0 - the value for which to solve for the corresponding x in the incomplete Beta integral.

Returns:

the value x such that incompleteBeta( a, b, x ) = y.

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