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 Details

    • 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