C Library Functions  - lamplt (3)

NAME
lamplt(3f) - [M_datapac:LINE_PLOT] generate a Tukey-Lambda probability plot

CONTENTS

Synopsis
Description
Options
Examples
Author
Maintainer
License
References

SYNOPSIS
SUBROUTINE LAMPLT(X,N,Alamba)

DESCRIPTION
lamplt(3f) generates a (tukey) lambda distribution probability plot (with tail length parameter value = alamba).

in general, the probability density function for this distribution is not simple.

the percent point function for this distribution is 

       g(p) = ((p**alamba)-((1-p)**alamba)) / alamba
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 lambda 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 lambda distribution with tail length parameter value = alamba.

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
X description of parameter
Y description of parameter

EXAMPLES
Sample program: 

   program demo_lamplt
   use M_datapac, only : lamplt
   implicit none
   ! call lamplt(x,y)
   end program demo_lamplt
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o FILLIBEN, SIMPLE AND ROBUST LINEAR ESTIMATION OF THE LOCATION PARAMETER OF A SYMMETRIC DISTRIBUTION (UNPUBLISHED PH.D. DISSERTATION, PRINCETON UNIVERSITY, 1969), pages 21-44, 229-231, pages 53-58.
o HASTINGS, MOSTELLER, TUKEY, AND WINDSOR, ’LOW MOMENTS FOR SMALL
SAMPLES:
  A COMPARATIVE STUDY OF ORDER STATISTICS’, ANNALS OF MATHEMATICAL STATISTICS, 18, 1947, pages 413-426.

Nemo Release 3.1 lamplt (3) February 23, 2025
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