C Library Functions - parcdf (3)

NAME

parcdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the Pareto cumulative distribution function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE PARCDF(X,Gamma,Cdf)

       REAL(kind=wp),intent(in)  :: X
       REAL(kind=wp),intent(in)  :: Gamma
       REAL(kind=wp),intent(out) :: Cdf

DESCRIPTION

PARCDF(3f) computes the cumulative distribution function value for the Pareto distribution with REAL tail length parameter = GAMMA.
The Pareto distribution used herein is defined for all X greater than or equal to 1, and has the probability density function
       f(X) = GAMMA / (X**(GAMMA+1))

INPUT ARGUMENTS

X The value at which the cumulative distribution function is to be evaluated. X should be greater than or equal to 1.

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

OUTPUT ARGUMENTS

CDF The cumulative distribution function value for the Pareto distribution

EXAMPLES

Sample program:

   program demo_parcdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : parcdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   real              :: gamma
   integer           :: i
      call label(’parcdf’)
      x=[(real(i)/10.0+1.0,i=1,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      gamma=0.3
      do i=1,size(x)
         call parcdf(X(i),Gamma,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_parcdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.1100000E+02 - X 0.1058750E+02 I XX 0.1017500E+02 I X 0.9762500E+01 I X 0.9350000E+01 I XX 0.8937500E+01 I X 0.8525000E+01 - X 0.8112500E+01 I XX 0.7700000E+01 I XX 0.7287500E+01 I XX 0.6875000E+01 I XX 0.6462500E+01 I XX 0.6050000E+01 - XX 0.5637500E+01 I XX 0.5225000E+01 I XXX 0.4812500E+01 I XX 0.4400000E+01 I XXX 0.3987500E+01 I XX 0.3575000E+01 - XX 0.3162500E+01 I XXX 0.2750000E+01 I XXX 0.2337501E+01 I XXXX 0.1925000E+01 I X XXX 0.1512500E+01 I X XX X 0.1100000E+01 - X X X I-----------I-----------I-----------I-----------I 0.2819E-01 0.1494E+00 0.2706E+00 0.3918E+00 0.5129E+00

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 233-249.

o hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 102.

Nemo Release 3.1

parcdf (3)

July 22, 2023

Generated by manServer 1.08 from c55e95e3-2946-492c-a169-d02e3882078a using man macros.

X	The value at which the cumulative distribution function is to be evaluated. X should be greater than or equal to 1.
GAMMA	The value of the tail length parameter. GAMMA should be positive.

o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 233-249.
o	hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 102.