smile.math.special

Class Beta

java.lang.Object

smile.math.special.Beta

public class Beta
extends java.lang.Object

The beta function, also called the Euler integral of the first kind.

B(x, y) = ∫₀¹ t^x-1 (1-t)^y-1dt

for x, y > 0 and the integration is over [0,1].The beta function is symmetric, i.e. B(x,y) = B(y,x).

Constructor Summary

Constructors

Constructor and Description
Beta()

Method Summary

Modifier and Type	Method and Description
static double	beta(double x, double y) Beta function, also called the Euler integral of the first kind.
static double	inverseRegularizedIncompleteBetaFunction(double alpha, double beta, double p) Inverse of regularized incomplete beta function.
static double	regularizedIncompleteBetaFunction(double alpha, double beta, double x) Regularized Incomplete Beta function.

Methods inherited from class java.lang.Object

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

Constructor Detail

Beta

public Beta()

Method Detail

beta

public static double beta(double x,
                          double y)

Beta function, also called the Euler integral of the first kind. The beta function is symmetric, i.e. B(x,y)==B(y,x).

regularizedIncompleteBetaFunction

public static double regularizedIncompleteBetaFunction(double alpha,
                                                       double beta,
                                                       double x)

Regularized Incomplete Beta function. Continued Fraction approximation (see Numerical recipies for details)

inverseRegularizedIncompleteBetaFunction

public static double inverseRegularizedIncompleteBetaFunction(double alpha,
                                                              double beta,
                                                              double p)

Inverse of regularized incomplete beta function.