Module statrs::function::gamma [−][src]
Expand description
Provides the gamma and related functions
Functions
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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