dev.nm.analysis.function.special.beta

Class BetaRegularized

java.lang.Object

dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

dev.nm.analysis.function.special.beta.BetaRegularized

All Implemented Interfaces:

Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class BetaRegularized
extends AbstractUnivariateRealFunction

The Regularized Incomplete Beta function is defined as: \[ I_x(p,q) = \frac{B(x;\,p,q)}{B(p,q)} = \frac{1}{B(p,q)} \int_0^x t^{p-1}\,(1-t)^{q-1}\,dt, p > 0, q > 0 \]

The R equivalent function is pbeta.

See Also:

• "Amparo Gil, Javier Segura, and Nico M. Temme. "Sections 6.7," Numerical Methods for Special Functions."
• Wikipedia: Incomplete beta function

Nested Class Summary

Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor and Description
BetaRegularized(double p, double q) Construct an instance of \(I_{x}(p,q)\) with the parameters p and q.

Method Summary

Modifier and Type	Method and Description
double	evaluate(double x) Evaluate \(I_{x}(p,q)\).
double	p() Get p, the shape parameter.
double	q() Get q, the shape parameter.

Methods inherited from class dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dimensionOfDomain, dimensionOfRange

Methods inherited from class java.lang.Object

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

Methods inherited from interface dev.nm.analysis.function.Function

dimensionOfDomain, dimensionOfRange

Constructor Detail

BetaRegularized

public BetaRegularized(double p,
                       double q)

Construct an instance of \(I_{x}(p,q)\) with the parameters p and q.

Parameters:

p - p > 0

q - q > 0

Method Detail

p

public double p()

Get p, the shape parameter.

Returns:

p

q

public double q()

Get q, the shape parameter.

Returns:

q

evaluate

public double evaluate(double x)

Evaluate \(I_{x}(p,q)\).

Parameters:

x - 0 ≤ x ≤ 1

Returns:

\(I_{x}(p,q)\)