Class RegularizedGamma.P

java.lang.Object
org.apache.commons.numbers.gamma.RegularizedGamma.P
Enclosing class:
RegularizedGamma

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

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

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    P()
    Prevent instantiation.
  • Method Summary

    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
  • Constructor Details

    • P

      private P()
      Prevent instantiation.
  • Method Details

    • 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