C Library Functions - tplt (3)

NAME

tplt(3f) - [M_datapac:LINE_PLOT] generates a Student’s T probability plot (with integer degrees of freedom parameter value NU).

Synopsis
Description
Input Arguments
Output
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE TPLT(X,N,Nu)

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

DESCRIPTION

TPLT(3f) generates a Student’s T probability plot (with integer degrees of freedom parameter value = NU).
The prototype Student’s T distribution used herein is defined for all 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 Student’s T 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 Student’s T 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. 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 Student’s T probability plot.

EXAMPLES

Sample program:

program demo_tplt use M_datapac, only : tplt implicit none ! call tplt(x,y) end program demo_tplt

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 National Bureau of Standards Applied Mathematics Series 55, 1964, page 949, FormulA 26.7.5.

o Johnson and Kotz, Continuous Univariate Distributions--2, 1970, page 102, Formula 11.

o Federighi, ’Extended Tables of the Percentage Points of Student’s T Distribution, Journal of the American Statistical Association, 1969, pages 683-688.

o Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 120-123.

Nemo Release 3.1

tplt (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. The maximum allowable value of N for this subroutine is 7500.
NU	The integer number of degrees of freedom. NU should be positive.

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	National Bureau of Standards Applied Mathematics Series 55, 1964, page 949, FormulA 26.7.5.
o	Johnson and Kotz, Continuous Univariate Distributions--2, 1970, page 102, Formula 11.
o	Federighi, ’Extended Tables of the Percentage Points of Student’s T Distribution, Journal of the American Statistical Association, 1969, pages 683-688.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 120-123.