Package smile.math.special

Class Gamma

java.lang.Object
smile.math.special.Gamma
public class Gamma extends Object
The gamma, digamma, and incomplete gamma functions.

  • Method Details

    • gamma

      public static double gamma(double x)
      Gamma function. Lanczos approximation (6 terms).
      Parameters:
      x - a real number.
      Returns:
      the function value.

    • lgamma

      public static double lgamma(double x)
      The log of the Gamma function. Lanczos approximation (6 terms)
      Parameters:
      x - a real number.
      Returns:
      the function value.

    • regularizedIncompleteGamma

      public static double regularizedIncompleteGamma(double s, double x)
      Regularized Incomplete Gamma Function P(s,x) = ∫0x e-t t(s-1) dt
      Parameters:
      s - s >= 0
      x - x >= 0
      Returns:
      the function value.

    • regularizedUpperIncompleteGamma

      public static double regularizedUpperIncompleteGamma(double s, double x)
      Regularized Upper/Complementary Incomplete Gamma Function Q(s,x) = 1 - P(s,x) = 1 - ∫0x e-t t(s-1) dt
      Parameters:
      s - s >= 0
      x - x >= 0
      Returns:
      the function value.

    • digamma

      public static double digamma(double x)
      The digamma function is defined as the logarithmic derivative of the gamma function.
      Parameters:
      x - a real number.
      Returns:
      the function value.

    • inverseRegularizedIncompleteGamma

      public static double inverseRegularizedIncompleteGamma(double a, double p)
      The inverse of regularized incomplete gamma function.
      Parameters:
      a - a > 0
      p - a real number.
      Returns:
      the function value.