Catalano.Math.Functions

Class Beta

java.lang.Object

Catalano.Math.Functions.Beta

public final class Beta
extends java.lang.Object

Beta functions.

Method Summary

Modifier and Type	Method and Description
static double	Function(double a, double b) Beta function as gamma(a) * gamma(b) / gamma(a+b).
static double	Incbcf(double a, double b, double x) Continued fraction expansion #1 for incomplete beta integral.
static double	Incbd(double a, double b, double x) Continued fraction expansion #2 for incomplete beta integral.
static double	Incomplete(double a, double b, double x) Incomplete (regularized) Beta function Ix(a, b).
static double	Log(double a, double b) Natural logarithm of the Beta function.
static double	PowerSeries(double a, double b, double x) Power series for incomplete beta integral.

Methods inherited from class java.lang.Object

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

Method Detail

Function

public static double Function(double a,
                              double b)

Beta function as gamma(a) * gamma(b) / gamma(a+b).

Parameters:

a - Value.

b - Value.

Returns:

Result.

Log

public static double Log(double a,
                         double b)

Natural logarithm of the Beta function.

Parameters:

a - Value.

b - Value.

Returns:

Result.

Incomplete

public static double Incomplete(double a,
                                double b,
                                double x)

Incomplete (regularized) Beta function Ix(a, b).

Parameters:

a - Value.

b - Value.

x - Value.

Returns:

Result.

Incbcf

public static double Incbcf(double a,
                            double b,
                            double x)

Continued fraction expansion #1 for incomplete beta integral.

Parameters:

a - Value.

b - Value.

x - Value.

Returns:

Result.

Incbd

public static double Incbd(double a,
                           double b,
                           double x)

Continued fraction expansion #2 for incomplete beta integral.

Parameters:

a - Value.

b - Value.

x - Value.

Returns:

Result.

PowerSeries

public static double PowerSeries(double a,
                                 double b,
                                 double x)

Power series for incomplete beta integral. Use when b*x is small and x not too close to 1.

Parameters:

a - Value.

b - Value.

x - Value.

Returns:

Result.