C Library Functions - weippf (3)

NAME

weippf(3f) - [M_datapac:PERCENT_POINT] compute the Weibull percent point function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE WEIPPF(P,Gamma,Ppf)

       REAL(kind=wp),intent(in)  :: P
       REAL(kind=wp),intent(in)  :: Gamma
       REAL(kind=wp),intent(out) :: Ppf

DESCRIPTION

WEIPPf(3f) computes the percent point function value for the Weibull distribution with REAL tail length parameter = GAMMA.
The Weibull distribution used herein is defined for all positive X, and has the probability density function
       f(X) = GAMMA * (X**(GAMMA-1)) * exp(-(X**GAMMA))
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.

GAMMA The value of the tail length parameter. GAMMA should be positive.

OUTPUT ARGUMENTS

PPF The percent point function value for the Weibull distribution

EXAMPLES

Sample program:

   program demo_weippf
   !@(#) line plotter graph of function
   use M_datapac, only : weippf, plott, label
   implicit none
   integer,parameter :: n=200
   real              :: x(n), y(n)
   real              :: gamma
   integer           :: i
      gamma=2.0
      call label(’weippf’)
      x=[(real(i)/real(n+1),i=1,n)]
      do i=1,n
         call weippf(x(i),gamma,y(i))
      enddo
      call plott(x,y,n)
   end program demo_weippf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.9950249E+00 - XX X X X 0.9537728E+00 I XXXXXX 0.9125207E+00 I XXXX 0.8712686E+00 I XXX 0.8300166E+00 I XXX 0.7887645E+00 I XX 0.7475125E+00 - XX 0.7062603E+00 I XX 0.6650083E+00 I XX 0.6237562E+00 I XX 0.5825042E+00 I XX 0.5412520E+00 I XX 0.5000000E+00 - XX 0.4587479E+00 I XX 0.4174958E+00 I XX 0.3762438E+00 I XX 0.3349917E+00 I XX 0.2937396E+00 I XX 0.2524875E+00 - XX 0.2112355E+00 I XX 0.1699834E+00 I XX 0.1287313E+00 I XX 0.8747923E-01 I XXX 0.4622716E-01 I XXX 0.4975124E-02 - XXX I-----------I-----------I-----------I-----------I 0.7062E-01 0.6287E+00 0.1187E+01 0.1745E+01 0.2303E+01

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 Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 250-271.

o Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 124.

Nemo Release 3.1

weippf (3)

February 23, 2025

Generated by manServer 1.08 from 52dd0a38-2d6e-4a58-afd2-8d2716131330 using man macros.

P	The value (between 0.0 (inclusively) and 1.0 (exclusively)) at which the percent point function is to be evaluated.
GAMMA	The value of the tail length parameter. GAMMA should be positive.

o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 250-271.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 124.