Package org.apache.commons.numbers.gamma

Class RegularizedGamma.Q

java.lang.Object

org.apache.commons.numbers.gamma.RegularizedGamma.Q

Enclosing class:

RegularizedGamma

public static final class RegularizedGamma.Q
extends Object

Upper regularized Gamma function \( Q(a, x) \).

\[ Q(a,x) = 1 - P(a,x) = \frac{\Gamma(a,x)}{\Gamma(a)} = \frac{1}{\Gamma(a)} \int_x^{\infty} t^{a-1}\,e^{-t}\,dt \]

Method Summary

Modifier and Type	Method	Description
static double	derivative(double a, double x)	Computes the derivative of the upper regularized gamma function \( Q(a, x) \).
static double	value(double a, double x)	Computes the upper regularized gamma function \( Q(a, x) \).
static double	value(double a, double x, double epsilon, int maxIterations)	Computes the upper regularized gamma function \( Q(a, x) \).

Methods inherited from class java.lang.Object

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

Method Detail

value

public static double value(double a,
                           double x)

Computes the upper regularized gamma function \( Q(a, x) \).

Parameters:

a - Argument.

x - Argument.

Returns:

\( Q(a, x) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.

value

public static double value(double a,
                           double x,
                           double epsilon,
                           int maxIterations)

Computes the upper regularized gamma function \( Q(a, x) \).

Parameters:

a - Argument.

x - Argument.

epsilon - Tolerance in series evaluation.

maxIterations - Maximum number of iterations in series evaluation.

Returns:

\( Q(a, x) \).

Throws:

ArithmeticException - if the series evaluation fails to converge.

derivative

public static double derivative(double a,
                                double x)

Computes the derivative of the upper regularized gamma function \( Q(a, x) \).

\[ \frac{\delta}{\delta x} Q(a,x) = -\frac{e^{-x} x^{a-1}}{\Gamma(a)} \]

This function has uses in some statistical distributions.

Parameters:

a - Argument.

x - Argument.

Returns:

derivative of \( Q(a,x) \) with respect to x.

Since:

1.1