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

Class BetaRegularizedInverse

java.lang.Object

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

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

All Implemented Interfaces:

Function<Vector,java.lang.Double>, RealScalarFunction, java.io.Serializable

public class BetaRegularizedInverse
extends UnivariateRealFunction

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)."

, Serialized Form

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.UnivariateRealFunction

dimensionOfDomain, dimensionOfRange, evaluate

Methods inherited from class java.lang.Object

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

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

Specified by:

evaluate in class UnivariateRealFunction

Parameters:

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

Returns:

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