Module statrs::function::gamma

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Provides the gamma and related functions

Functions

  • checked_gamma_li
    Computes the lower incomplete gamma function gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.
  • checked_gamma_lr
    Computes the lower incomplete regularized gamma function P(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for real a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.
  • checked_gamma_ui
    Computes the upper incomplete gamma function Gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower intergral limit.
  • checked_gamma_ur
    Computes the upper incomplete regularized gamma function Q(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower integral limit.
  • digamma
    Computes the Digamma function which is defined as the derivative of the log of the gamma function. The implementation is based on “Algorithm AS 103”, Jose Bernardo, Applied Statistics, Volume 25, Number 3 1976, pages 315 - 317
  • gamma
    Computes the gamma function with an accuracy of 16 floating point digits. The implementation is derived from “An Analysis of the Lanczos Gamma Approximation”, Glendon Ralph Pugh, 2004 p. 116
  • gamma_li
    Computes the lower incomplete gamma function gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.
  • gamma_lr
    Computes the lower incomplete regularized gamma function P(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for real a > 0, x > 0 where a is the argument for the gamma function and x is the upper integral limit.
  • gamma_ui
    Computes the upper incomplete gamma function Gamma(a,x) = int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower intergral limit.
  • gamma_ur
    Computes the upper incomplete regularized gamma function Q(a,x) = 1 / Gamma(a) * int(exp(-t)t^(a-1), t=0..x) for a > 0, x > 0 where a is the argument for the gamma function and x is the lower integral limit.
  • inv_digamma
  • ln_gamma
    Computes the logarithm of the gamma function with an accuracy of 16 floating point digits. The implementation is derived from “An Analysis of the Lanczos Gamma Approximation”, Glendon Ralph Pugh, 2004 p. 116