C Library Functions  - hfnplt (3)

NAME
hfnplt(3f) - [M_datapac:LINE_PLOT] generate a half-normal probability plot

CONTENTS

Synopsis
Description
Options
Input Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS
SUBROUTINE HFNPLT(X,N) 

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

DESCRIPTION
HFNPLT(3f) generates a halfnormal probability plot.

The prototype halfnormal distribution used herein has mean = sqrt(2/pi) = 0.79788456 and standard deviation = 1.

This distribution is defined for all non-negative X and has the probability density function 

       f(X) = (2/sqrt(2*pi)) * exp(-X*X/2)
The prototype halfnormal distribution used herein is the distribution of the variate X = abs(Z) where the variate Z is normally distributed with mean = 0 and standard deviation = 1.

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 halfnormal 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 halfnormal distribution.

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.

OPTIONS

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.

OUTPUT
A one-page halfnormal probability plot.

EXAMPLES
Sample program: 

   program demo_hfnplt
   use M_datapac, only : hfnplt
   implicit none
   ! call hfnplt(x,y)
   end program demo_hfnplt
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 Daniel, ’Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments’, Technometrics, 1959, pages 311-341.
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 53, 59, 81, 83.

Nemo Release 3.1 hfnplt (3) February 23, 2025
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