C Library Functions  - gamcdf (3)

NAME
gamcdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the gamma cumulative distribution function

CONTENTS

Synopsis
Description
Accuracy
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS
SUBROUTINE GAMCDF(X,Gamma,Cdf) 

       REAL(kind=wp),intent(in)  :: Gamma
       REAL(kind=wp),intent(in)  :: X
       REAL(kind=wp),intent(out) :: Cdf

DESCRIPTION
GAMCDF(3f) computes the cumulative distribution function value for the gamma distribution with REAL tail length parameter = GAMMA.

The Gamma distribution used herein has mean = GAMMA and standard deviation = sqrt(GAMMA).

This distribution is defined for all positive X, and has the probability density function 

       f(X) = (1/constant) * (X**(GAMMA-1)) * exp(-X)
Where the constant = the Gamma function evaluated at the value GAMMA.

Note the mode of internal operations is DOUBLE PRECISION.

ACCURACY

(On the UNIVAC 1108, EXEC 8 system at NBS) 

   Compared to the known GAMMA = 1 (exponential) results, agreement
   was had out to 7 significant digits for all tested X. The tested X
   values covered the entire range of the distribution--from the 0.00001
   percent point up to the 99.99999 percent point of the distribution.

INPUT ARGUMENTS
X The value at which the cumulative distribution function is to be evaluated. X should be positive.
GAMMA The value of the tail length parameter. GAMMA should be positive.

OUTPUT ARGUMENTS

CDF The cumulative distribution function value for the gamma distribution

EXAMPLES
Sample program: 

   program demo_gamcdf
   use M_datapac, only : gamcdf
   implicit none
   ! call gamcdf(x,y)
   end program demo_gamcdf
Results:

AUTHOR
The original DATAPAC library was written by James Filliben of the Statistical Engineering Division, National Institute of Standards and Technology.

MAINTAINER
John Urban, 2022.05.31

LICENSE
CC0-1.0

REFERENCES
o WILK, GNANADESIKAN, AND HUYETT, ’PROBABILITY PLOTS FOR THE GAMMA DISTRIBUTION’, TECHNOMETRICS, 1962, pages 1-15, ESPECIALLY pages 3-5.
o NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS SERIES 55, 1964, page 257, FORMULA 6.1.41.
o JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE DISTRIBUTIONS--1, 1970, pages 166-206.
o HASTINGS AND PEACOCK, STATISTICAL DISTRIBUTIONS--A HANDBOOK FOR STUDENTS AND PRACTITIONERS, 1975, pages 68-73.

Nemo Release 3.1 gamcdf (3) February 23, 2025
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