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

java.lang.Object
  com.numericalmethod.suanshu.analysis.function.rn2r1.BivariateRealFunction
      com.numericalmethod.suanshu.analysis.function.special.GammaRegularizedPInverse

All Implemented Interfaces:

Function, RealScalarFunction

public class GammaRegularizedPInverse
extends BivariateRealFunction

This class represents the inverse of the Regularized Incomplete Gamma P function.

x = P-1(s, u)

, where

0 ≤ u ≤ 1

• When s > 1, the algorithm used is 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

Nested Class Summary

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

Function.EvaluationException

Constructor Summary

GammaRegularizedPInverse()

Method Summary

double

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

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

dimension4Domain, dimension4Range, 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)