org.apache.commons.math.special
Class Beta

java.lang.Object
  org.apache.commons.math.special.Beta

All Implemented Interfaces:

Serializable

public class Beta

extends Object

implements Serializable

This is a utility class that provides computation methods related to the Beta family of functions.

Version:

$Revision: 1.21 $ $Date: 2004/06/23 16:26:17 $

See Also:

Serialized Form

Method Summary

static double	logBeta(double a, double b) Returns the natural logarithm of the beta function B(a, b).
static double	logBeta(double a, double b, double epsilon, int maxIterations) Returns the natural logarithm of the beta function B(a, b).
static double	regularizedBeta(double x, double a, double b) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, double epsilon) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, double epsilon, int maxIterations) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, int maxIterations) Returns the regularized beta function I(x, a, b).

Methods inherited from class java.lang.Object

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

Method Detail

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b)
                              throws MathException

Returns the regularized beta function I(x, a, b).

Parameters:

x - the value.

a - the a parameter.

b - the b parameter.

Returns:

the regularized beta function I(x, a, b)

Throws:

MathException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     double epsilon)
                              throws MathException

Returns the regularized beta function I(x, a, b).

Parameters:

x - the value.

a - the a parameter.

b - the b parameter.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

Returns:

the regularized beta function I(x, a, b)

Throws:

MathException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     int maxIterations)
                              throws MathException

Returns the regularized beta function I(x, a, b).

Parameters:

x - the value.

a - the a parameter.

b - the b parameter.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized beta function I(x, a, b)

Throws:

MathException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     double epsilon,
                                     int maxIterations)
                              throws MathException

Returns the regularized beta function I(x, a, b). The implementation of this method is based on:

• Regularized Beta Function.
• Regularized Beta Function.

Parameters:

x - the value.

a - the a parameter.

b - the b parameter.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized beta function I(x, a, b)

Throws:

MathException - if the algorithm fails to converge.

logBeta

public static double logBeta(double a,
                             double b)

Returns the natural logarithm of the beta function B(a, b).

Parameters:

a - the a parameter.

b - the b parameter.

Returns:

log(B(a, b))

logBeta

public static double logBeta(double a,
                             double b,
                             double epsilon,
                             int maxIterations)

Returns the natural logarithm of the beta function B(a, b). The implementation of this method is based on:

• Beta Function, equation (1).

Parameters:

a - the a parameter.

b - the b parameter.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

log(B(a, b))