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C Library Functions  - tail (3)

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NAME

tail(3f) - [M_datapac:ANALYSIS] performs a symmetric distribution tail length analysis

CONTENTS

Synopsis
Description
Input Arguments
Output
Examples
Author
Maintainer
License
Reference

SYNOPSIS

SUBROUTINE TAIL(X,N)

       REAL(kind=wp) :: X(:)
       INTEGER       :: N

DESCRIPTION

TAIL(3f) performs a symmetric distribution tail length analysis on the data in the input vector X.

The analysis consists of the following--

1.	Various test statistics to test the specific hypothesis of normality;
2.	A uniform probability plot (a short-tailed distribution);
3.	A normal probability plot (a moderate-tailed distribution);
4.	A tukey lambda = -0.5 probability plot (a moderate-long-tailed distribution);
5.	A cauchy probability plot (a long-tailed distribution);
6.	A determination of the best-fit symmetric distribution to the data set from an admissible set consisting of 43 symmetric distributions.

The admissible set of symmetric distributions considered includes the uniform, normal, logistic, double exponential, cauchy, and 37 distributions drawn from the the tukey lambda distributional family.

The goodness of fit criterion is the maximum probability plot correlation coefficient criterion.

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 3000.

OUTPUT

6 pages of automatic printout--

1.	various test statistics for normality;
2.	a uniform probability plot;
3.	a normal probability plot;
4.	a tukey lambda = -0.5 probability plot;
5.	a cauchy probability plot;
6.	a determination of the best-fit symmetric distribution to the data set.

EXAMPLES

Sample program:

   program demo_tail
   use M_datapac, only : tail, label
   implicit none
   real,allocatable :: x(:)
   integer :: i
      call label(’tail’)
      x=[(real(i)/10.0,i=1,2000)]
      x=x**3.78-6*x**2.52+9*x**1.26
      call tail(x,size(x))
   end program demo_tail

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

REFERENCE

o	Filliben (1972), ’Techniques for Tail Length Analysis’, Proceedings of the Eighteenth Conference on the Design of Experiments in Army Research and Testing, pages 425-450.
o	Filliben, ’The Percent Point Function’, Unpublished Manuscript.
o	Johnson and Kotz (1970), Continuous Univariate Distributions-1, pages 250-271.

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Nemo Release 3.1

tail (3)

February 23, 2025

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