C Library Functions - unimed (3)
NAME
unimed(3f) - [M_datapac:STATISTICS] generates the N order statistic medians from the uniform (rectangular) distribution on the unit interval (0,1).
CONTENTS
Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References
SYNOPSIS
SUBROUTINE UNIMED(N,X)
INTEGER,intent(in) :: N REAL(kind=wp),intent(out) :: X(:)
DESCRIPTION
UNIMED(3f) generates the N order statistic medians from the uniform (rectangular) distribution on the unit interval (0,1).
This distribution has mean = 0.5 and standard deviation = sqrt(1/12) = 0.28867513. This distribution has the probability density function f(X) = 1.
UNIMED(3f) is a support subroutine for all of the probability plot subroutines in datapac; it is rarely used by the data analyst directly.
A probability plot for a general distribution is a plot of the ordered observations versus the order statistic medians for that distribution.
The i-th order statistic median for a general distribution is obtained by transforming the i-th uniform order statistic median by the percent point function of the desired distribution--hence the importance of being able to generate uniform order statistic medians.
It is of theoretical interest to note that the i-th uniform order statistic median in a sample of size N is identically the median of the beta distribution with parameters i and N-i+1.
INPUT ARGUMENTS
N The desired integer number of uniform order statistic medians to be generated.
OUTPUT ARGUMENTS
X A vector (of dimension at least N) into which the generated uniform order statistic medians will be placed.
EXAMPLES
Sample program:
program demo_unimed use M_datapac, only : unimed, label, plotxt implicit none integer,parameter :: N=100 real :: X(N) call label(’unimed’) call unimed(N,X) call plotxt(x,n) end program demo_unimedResults:
THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY I-----------I-----------I-----------I-----------I 0.9930925E+00 - XX 0.9520015E+00 I XXX 0.9109104E+00 I XXX 0.8698193E+00 I XXX 0.8287283E+00 I XXX 0.7876373E+00 I XXX 0.7465463E+00 - XXX 0.7054552E+00 I XXX 0.6643642E+00 I XXX 0.6232731E+00 I XXX 0.5821820E+00 I XXX 0.5410910E+00 I XXX 0.5000000E+00 - XXX 0.4589090E+00 I XXX 0.4178179E+00 I XXX 0.3767269E+00 I XXX 0.3356358E+00 I XXX 0.2945448E+00 I XXX 0.2534538E+00 - XXX 0.2123627E+00 I XXX 0.1712717E+00 I XXX 0.1301807E+00 I XXX 0.8908957E-01 I XXX 0.4799855E-01 I XXX 0.6907523E-02 - XX I-----------I-----------I-----------I-----------I 0.1000E+01 0.2575E+02 0.5050E+02 0.7525E+02 0.1000E+03
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, ’The Probability Plot Correlation Coefficient Test for Normality’, Technometrics, 1975, pages 111-117.
| Nemo Release 3.1 | unimed (3) | February 23, 2025 |
