## Class RegularizedGamma.P

• Enclosing class:
RegularizedGamma

public static final class RegularizedGamma.P
extends Object
Lower regularized Gamma function $$P(a, x)$$.

$P(a,x) = 1 - Q(a,x) = \frac{\gamma(a,x)}{\Gamma(a)} = \frac{1}{\Gamma(a)} \int_0^x t^{a-1}\,e^{-t}\,dt$

• ### Method Summary

All Methods
Modifier and Type Method Description
static double derivative​(double a, double x)
Computes the derivative of the lower regularized gamma function $$P(a, x)$$.
static double value​(double a, double x)
Computes the lower regularized gamma function $$P(a, x)$$.
static double value​(double a, double x, double epsilon, int maxIterations)
Computes the lower regularized gamma function $$P(a, x)$$.
• ### 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 lower regularized gamma function $$P(a, x)$$.
Parameters:
a - Argument.
x - Argument.
Returns:
$$P(a, x)$$.
Throws:
ArithmeticException - if the continued fraction fails to converge.
• #### value

public static double value​(double a,
double x,
double epsilon,
int maxIterations)
Computes the lower regularized gamma function $$P(a, x)$$.
Parameters:
a - Argument.
x - Argument.
epsilon - Tolerance in series evaluation.
maxIterations - Maximum number of iterations in series evaluation.
Returns:
$$P(a, x)$$.
Throws:
ArithmeticException - if the series evaluation fails to converge.
• #### derivative

public static double derivative​(double a,
double x)
Computes the derivative of the lower regularized gamma function $$P(a, x)$$.

$\frac{\delta}{\delta x} P(a,x) = \frac{e^{-x} x^{a-1}}{\Gamma(a)}$

This function has uses in some statistical distributions.

Parameters:
a - Argument.
x - Argument.
Returns:
derivative of $$P(a,x)$$ with respect to x.
Since:
1.1