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C Library Functions  - cauplt (3)

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NAME

cauplt(3f) - [M_datapac:LINE_PLOT] generate a Cauchy probability plot

CONTENTS

Synopsis
Description
Input Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE CAUPLT(X,N)

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

DESCRIPTION

CAUPLT(3f) generates a one-page Cauchy probability plot.

The prototype Cauchy distribution used herein has median = 0 and 75% point = 1.

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

       f(X) = (1/pi) * (1/(1+X*X))

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 Cauchy 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 Cauchy 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.

INPUT ARGUMENTS

X	The vector of (unsorted or sorted) observations.
N	The integer number of observations in the vector X.

OUTPUT

A one-page Cauchy probability plot.

EXAMPLES

Sample program:

   program demo_cauplt
   use M_datapac, only : cauplt
   implicit none
   ! call cauplt(x,y)
   end program demo_cauplt

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	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 154-165.

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Nemo Release 3.1

cauplt (3)

February 23, 2025

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