C Library Functions - chsppf (3)

NAME

chsppf(3f) - [M_datapac:PERCENT_POINT] compute the chi-square percent point function

Synopsis
Description
Input Arguments
Output Arguments
Accuracy
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE CHSPPF(P,Nu,Ppf)

       REAL(kind=wp) :: P
       REAL(kind=wp) :: Ppf
       INTEGER       :: Nu

DESCRIPTION

CHSPPF(3f) computes the percent point function value for the chi-squared distribution with integer degrees of freedom parameter = nu.
The chi-squared distribution used herein is defined for all non-negative x, and its probability density function is given in references 2, 3, and 4 below.
Note that the percent point function of a distribution is identically the same as the inverse cumulative distribution function of the distribution.

INPUT ARGUMENTS

P The value (between 0.0 (inclusively) and 1.0 (exclusively)) at which the percent point function is to be evaluated.

NU The integer number of degrees of freedom. NU should be positive.

OUTPUT ARGUMENTS

PPF The percent point function value for the chi-squared distribution

ACCURACY

(On the UNIVAC 1108, EXEC 8 System at NBS) Compared to the known NU = 2 (exponential) results, agreement was had out to 6 significant

digits for all tested P in the range P = .001 to P = .999.
for P = [char46]95 And smaller, The agreement was even better--7 significant digits. (Note that the tabulated values given in the Wilk, Gnanadesikan, and Huyett reference below, page 20, are in error for at least the GAMMA = 1 case-- The worst detected error was agreement to only 3 significant digits (in their 8 significant digit table) for P = .999.)

EXAMPLES

Sample program:

program demo_chsppf use M_datapac, only : chsppf implicit none ! call chsppf(x,y) end program demo_chsppf

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 Wilk, gnanadesikan, and huyett, ’probability plots for the gamma Distribution’, technometrics, 1962, pages 1-15, especially pages 3-5.

o National bureau of standards applied mathematics series 55, 1964, page 257, formula 6.1.41, and pages 940-943.

o Johnson and kotz, continuous univariate distributions--1, 1970, pages 166-206.

o Hastings and peacock, statistical distributions--a handbook for Students and practitioners, 1975, pages 46-51.

Nemo Release 3.1

chsppf (3)

July 22, 2023

Generated by manServer 1.08 from 50c5125b-8fc1-4979-9240-5decff623130 using man macros.

P	The value (between 0.0 (inclusively) and 1.0 (exclusively)) at which the percent point function is to be evaluated.
NU	The integer number of degrees of freedom. NU should be positive.

digits for all tested P in the range P = .001 to P = .999.
	for P = [char46]95 And smaller, The agreement was even better--7 significant digits. (Note that the tabulated values given in the Wilk, Gnanadesikan, and Huyett reference below, page 20, are in error for at least the GAMMA = 1 case-- The worst detected error was agreement to only 3 significant digits (in their 8 significant digit table) for P = .999.)

o	Wilk, gnanadesikan, and huyett, ’probability plots for the gamma Distribution’, technometrics, 1962, pages 1-15, especially pages 3-5.
o	National bureau of standards applied mathematics series 55, 1964, page 257, formula 6.1.41, and pages 940-943.
o	Johnson and kotz, continuous univariate distributions--1, 1970, pages 166-206.
o	Hastings and peacock, statistical distributions--a handbook for Students and practitioners, 1975, pages 46-51.