C Library Functions - chsplt (3)

NAME

chsplt(3f) - [M_datapac:LINE_PLOT] generate a Chi-square probability plot

Synopsis
Description
Input Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE CHSPLT(X,N,Nu)

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

DESCRIPTION

Chsplt(3f) generates a Chi-squared probability plot (with integer degrees of freedom parameter value = NU).
The prototype Chi-squared distribution used herein is defIned for all non-negative X, and its probability density function is given in the references below.
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 Chi-squared 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 Chi-squared distribution with degrees of freedom parameter value = NU.
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. NU should be positive. The maximum allowable value of N for this subroutine is 7500.

NU The integer number of degrees of freedom. NU should be positive.

OUTPUT

A one-page Chi-squared probability plot.

EXAMPLES

Sample program:

program demo_chsplt use M_datapac, only : chsplt implicit none ! call chsplt(x,y) end program demo_chsplt

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 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.

o Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 46-51.

Nemo Release 3.1

chsplt (3)

July 22, 2023

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X	The vector of (unsorted or sorted) observations.
N	The integer number of observations in the vector X. NU should be positive. The maximum allowable value of N for this subroutine is 7500.
NU	The integer number of degrees of freedom. NU should be positive.

o	Wilk, Gnanadesikan, and Huyett, ’Probability Plots for the Gamma Distribution’, Technometrics, 1962, pages 1-15.
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.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 46-51.