com.numericalmethod.suanshu.analysis.function.special.beta

Class BetaRegularizedInverse

java.lang.Object

com.numericalmethod.suanshu.analysis.function.rn2r1.AbstractRealScalarFunction

com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

com.numericalmethod.suanshu.analysis.function.special.beta.BetaRegularizedInverse

All Implemented Interfaces:

Function<Vector,Double>, RealScalarFunction, UnivariateRealFunction

public class BetaRegularizedInverse
extends AbstractUnivariateRealFunction

The inverse of the Regularized Incomplete Beta function is defined at: \[ x = I^{-1}_{(p,q)}(u), 0 \le u \le 1 \]

The R equivalent function is qbeta.

See Also:

• "Amparo Gil, Javier Segura, and Nico M. Temme, "Section 10.5," Numerical Methods for Special Functions."
• "John Maddock, Paul A. Bristow, Hubert Holin, and Xiaogang Zhang. "Notes for The Incomplete Beta Function Inverses," Boost Library."
• "K. L. Majumder, and G. P. Bhattacharjee, Algorithm AS 63: The Incomplete Beta Integral, 1973."
• "Cran, G. W., K. J. Martin, and G. E. Thomas, "Remark AS R19 and Algorithm AS 109," Applied Statistics, 26, 111-114, 1977, and subsequent remarks (AS83 and correction)."

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor and Description
BetaRegularizedInverse(double p, double q) Construct an instance of \(I^{-1}_{(p,q)}(u)\) with parameters p and p.

Method Summary

Modifier and Type	Method and Description
double	evaluate(double u) Evaluate \(I^{-1}_{(p,q)}(u)\).

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

Methods inherited from class com.numericalmethod.suanshu.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 com.numericalmethod.suanshu.analysis.function.Function

dimensionOfDomain, dimensionOfRange

Constructor Detail

BetaRegularizedInverse

public BetaRegularizedInverse(double p,
                              double q)

Construct an instance of \(I^{-1}_{(p,q)}(u)\) with parameters p and p.

Parameters:

p - p > 0

q - q > 0

Method Detail

evaluate

public double evaluate(double u)

Evaluate \(I^{-1}_{(p,q)}(u)\).

Parameters:

u - \(0 \le u \le 1\)

Returns:

\(I^{-1}_{(p,q)}(u)\)