com.numericalmethod.suanshu.analysis.function.special.gamma

Class GammaRegularizedPInverse

java.lang.Object

com.numericalmethod.suanshu.analysis.function.rn2r1.BivariateRealFunction

com.numericalmethod.suanshu.analysis.function.special.gamma.GammaRegularizedPInverse

All Implemented Interfaces:

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

public class GammaRegularizedPInverse
extends BivariateRealFunction

The inverse of the Regularized Incomplete Gamma P function is defined as: \[ x = P^{-1}(s,u), 0 \geq u \geq 1 \]

• When s > 1, we use the asymptotic inversion method.
• When s <= 1, we use an approximation of P(s,x) together with a higher-order Newton like method.

In both cases, the estimated value is then improved using Halley's method, c.f., Halley

The R equivalent function is qgamma. E.g., qgamma(u, s, lower=TRUE).

See Also:

• "Amparo Gil, Javier Segura, and Nico M. Temme. "Sections 8.3, 10.3.1, 10.6," Numerical Methods for Special Functions."
• Wikipedia: Regularized Gamma functions and Poisson random variables

, 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
GammaRegularizedPInverse()

Method Summary

Modifier and Type	Method and Description
double	evaluate(double s, double u) Evaluate x = P-1(s,u).

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.BivariateRealFunction

dimensionOfDomain, dimensionOfRange, evaluate

Methods inherited from class java.lang.Object

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

Constructor Detail

GammaRegularizedPInverse

public GammaRegularizedPInverse()

Method Detail

evaluate

public double evaluate(double s,
                       double u)

Evaluate x = P^-1(s,u).

Specified by:

evaluate in class BivariateRealFunction

Parameters:

s - s > 0

u - 0 ≤ u ≤ 1

Returns:

P^-1(s,u)