C Library Functions - gamplt (3)

NAME

gamplt(3f) - [M_datapac:LINE_PLOT] generate a gamma probability plot

Synopsis
Description
Input Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE GAMPLT(X,N,Gamma)

       REAL(kind=wp),intent(in) :: X(:)
       INTEGER,intent(in)       :: N
       REAL(kind=wp),intent(in) :: Gamma

DESCRIPTION

GAMPLT(3f) generates a gamma probability plot (with tail length parameter value = GAMMA).
The prototype 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.
As used herein, a probability plot for a distribution is a plot of the ordered observations versus the order statistic medians for that distribution.
The gamma probability plot is useful in graphically testing the composite (that is, location and scale parameters need not be specified) hypothesis that the underlying distribution from which the data have been randomly drawn is the gamma distribution with tail length parameter value = GAMMA.
If the hypothesis is true, the probability plot should be near-linear.
A measure of such linearity is given by the calculated probability plot correlation coefficient.

INPUT ARGUMENTS

X The vector of (unsorted or sorted) observations.

N The integer number of observations in the vector X. The maximum allowable value of N for this subroutine is 7500.

GAMMA The value of the tail length parameter. Gamma should be positive.

OUTPUT

A one-page gamma probability plot.

EXAMPLES

Sample program:

program demo_gamplt use M_datapac, only : gamplt implicit none ! call gamplt(x,y) end program demo_gamplt

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.

o National Bureau of Standards Applied Mathematics Series 55, 1964, page 257, Formula 6.1.41.

o Filliben, ’Techniques for Tail Length Analysis’, Proceedings of the Eighteenth Conference on the Design of Experiments in Army Research Development and Testing (Aberdeen, Maryland, October, 1972), pages 425-450.

o Hahn and Shapiro, Statistical Methods in Engineering, 1967, pages 260-308.

o Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 166-206.

Nemo Release 3.1

gamplt (3)

July 22, 2023

Generated by manServer 1.08 from a750acf1-22ca-43de-a35c-bcdaf2075658 using man macros.

X	The vector of (unsorted or sorted) observations.
N	The integer number of observations in the vector X. The maximum allowable value of N for this subroutine is 7500.
GAMMA	The value of the tail length parameter. Gamma should be positive.

o	Wilk, Gnanadesikan, and Huyett, ’Probability Plots for the Gamma Distribution’, Technometrics, 1962, pages 1-15.
o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 257, Formula 6.1.41.
o	Filliben, ’Techniques for Tail Length Analysis’, Proceedings of the Eighteenth Conference on the Design of Experiments in Army Research Development and Testing (Aberdeen, Maryland, October, 1972), pages 425-450.
o	Hahn and Shapiro, Statistical Methods in Engineering, 1967, pages 260-308.
o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 166-206.