Package org.apache.commons.numbers.gamma

Class IncompleteBeta

java.lang.Object

org.apache.commons.numbers.gamma.IncompleteBeta

public final class IncompleteBeta
extends Object

Incomplete Beta function.

\[ B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt \]

This code has been adapted from the Boost c++ implementation <boost/math/special_functions/beta.hpp>.

Since:

1.1

See Also:

Boost C++ Incomplete Beta functions

Method Summary

Modifier and Type	Method	Description
static double	complement(double x, double a, double b)	Computes the complement of the incomplete beta function B(x, a, b).
static double	complement(double x, double a, double b, double epsilon, int maxIterations)	Computes the complement of the incomplete beta function B(x, a, b).
static double	value(double x, double a, double b)	Computes the value of the incomplete beta function B(x, a, b).
static double	value(double x, double a, double b, double epsilon, int maxIterations)	Computes the value of the incomplete beta function B(x, a, b).

Methods inherited from class java.lang.Object

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

Method Detail

value

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

Computes the value of the incomplete beta function B(x, a, b).

\[ B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt \]

Parameters:

x - Value.

a - Parameter a.

b - Parameter b.

Returns:

the incomplete beta function \( B_x(a, b) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.

value

public static double value(double x,
                           double a,
                           double b,
                           double epsilon,
                           int maxIterations)

Computes the value of the incomplete beta function B(x, a, b).

\[ B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt \]

Parameters:

x - the value.

a - Parameter a.

b - Parameter b.

epsilon - Tolerance in series evaluation.

maxIterations - Maximum number of iterations in series evaluation.

Returns:

the incomplete beta function \( B_x(a, b) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.

complement

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

Computes the complement of the incomplete beta function B(x, a, b).

\[ B(a, b) - B_x(a,b) = B_{1-x}(b, a) \]

where \( B(a, b) \) is the beta function.

Parameters:

x - Value.

a - Parameter a.

b - Parameter b.

Returns:

the complement of the incomplete beta function \( B(a, b) - B_x(a, b) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.

complement

public static double complement(double x,
                                double a,
                                double b,
                                double epsilon,
                                int maxIterations)

Computes the complement of the incomplete beta function B(x, a, b).

\[ B(a, b) - B_x(a,b) = B_{1-x}(b, a) \]

where \( B(a, b) \) is the beta function.

Parameters:

x - the value.

a - Parameter a.

b - Parameter b.

epsilon - Tolerance in series evaluation.

maxIterations - Maximum number of iterations in series evaluation.

Returns:

the complement of the incomplete beta function \( B(a, b) - B_x(a, b) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.