org.hipparchus.special

## Class Beta

• public class Beta
extends Object

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

Implementation of logBeta(double, double) is based on the algorithms described in

and implemented in the NSWC Library of Mathematical Functions, available here. This library is "approved for public release", and the Copyright guidance indicates that unless otherwise stated in the code, all FORTRAN functions in this library are license free. Since no such notice appears in the code these functions can safely be ported to Hipparchus.

• ### Method Summary

All Methods
Modifier and Type Method and Description
static double logBeta(double p, double q)
Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0.
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)
Returns the regularized beta function I(x, a, b).
Parameters:
x - Value.
a - Parameter a.
b - Parameter b.
Returns:
the regularized beta function I(x, a, b).
Throws:
MathIllegalStateException - if the algorithm fails to converge.
• #### regularizedBeta

public static double regularizedBeta(double x,
double a,
double b,
double epsilon)
Returns the regularized beta function I(x, a, b).
Parameters:
x - Value.
a - Parameter a.
b - Parameter b.
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:
MathIllegalStateException - if the algorithm fails to converge.
• #### regularizedBeta

public static double regularizedBeta(double x,
double a,
double b,
int maxIterations)
Returns the regularized beta function I(x, a, b).
Parameters:
x - the value.
a - Parameter a.
b - Parameter b.
maxIterations - Maximum number of "iterations" to complete.
Returns:
the regularized beta function I(x, a, b)
Throws:
MathIllegalStateException - if the algorithm fails to converge.
• #### regularizedBeta

public static double regularizedBeta(double x,
double a,
double b,
double epsilon,
int maxIterations)
Returns the regularized beta function I(x, a, b). The implementation of this method is based on:
Parameters:
x - the value.
a - Parameter a.
b - Parameter b.
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:
MathIllegalStateException - if the algorithm fails to converge.
• #### logBeta

public static double logBeta(double p,
double q)
Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the NSWC Library of Mathematics Subroutines implementation, DBETLN.
Parameters:
p - First argument.
q - Second argument.
Returns:
the value of log(Beta(p, q)), NaN if p <= 0 or q <= 0.