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

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

All Implemented Interfaces:

Function, RealScalarFunction

public class GammaRegularizedQ
extends BivariateRealFunction

This class represents the Regularized Incomplete Gamma Q function Q(s, x).

Γ(s, x) Q(s, x) = ----------- = 1 - P(s, x) Γ(s)

s ≥ 0, x ≥ 0 The algorithm for computing the regularized incomplete Gamma Q function depends on the values of s and x.

• For s > 100, Q is approximated using the Gauss-Legendre quadrature.
• For x < s + 1, Q is approximated by the Pearson's series representation.
• Otherwise, Q is approximated by the continued fraction due to Legendre.

The R equivalent function is pgamma. E.g., pgamma(x, s, lower=FALSE).

See Also:

• "B Shea." Algorithm AS 239: Chi-squared and Incomplete Gamma Integral," Applied Statistics. Volume 37, Number 3, 1988, pages 466-473."
• 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

GammaRegularizedQ()

Method Summary

double

evaluate(double s, double x) Evaluate Q(s, x).

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

GammaRegularizedQ

public GammaRegularizedQ()

Method Detail

evaluate

public double evaluate(double s,
                       double x)

Evaluate Q(s, x).

Specified by:

evaluate in class BivariateRealFunction

Parameters:

s - s ≥ 0

x - x ≥ 0

Returns:

Q(s, x)