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C Library Functions  - parran (3)

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NAME

parran(3f) - [M_datapac:RANDOM] generate Pareto random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE PARRAN(N,Gamma,Iseed,X)

       INTEGER       :: N
       REAL(kind=wp) :: Gamma
       INTEGER       :: Iseed
       REAL(kind=wp) :: X(:)

DESCRIPTION

PARRAN(3f) generates a random sample of size N from the Pareto distribution with tail length parameter value = GAMMA.

The prototype 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

N	The desired integer number of random numbers to be generated.
GAMMA	The value of the tail length parameter. GAMMA should be positive.
ISEED	An integer seed value. Should be set to a non-negative value to start a new sequence of values. Will be set to -1 on return to indicate the next call should continue the current random sequence walk.

OUTPUT ARGUMENTS

X	A vector (of dimension at least N) into which the generated random sample from the Pareto distribution will be placed.

EXAMPLES

Sample program:

   program demo_parran
   use m_datapac, only : parran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=4000
   real :: x(n)
   integer :: iseed
   real :: gamma
      call label(’parran’)
      gamma=3.4
      iseed=12345
      call parran(n,gamma,iseed,x)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_parran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1956372E+02 -   X
     0.1879024E+02 I
     0.1801675E+02 I
     0.1724326E+02 I
     0.1646978E+02 I
     0.1569629E+02 I
     0.1492280E+02 -
     0.1414931E+02 I
     0.1337583E+02 I
     0.1260234E+02 I
     0.1182885E+02 I
     0.1105537E+02 I                   X
     0.1028188E+02 -
     0.9508391E+01 I
     0.8734904E+01 I                          X
     0.7961417E+01 I                                    X
     0.7187930E+01 I
     0.6414443E+01 I                  X X                 X  XX
     0.5640956E+01 -           X                  XX          XX
     0.4867469E+01 I   X        X X X XX X          X         X X
     0.4093982E+01 I    X X             X    XX X XX   X   X  X    X X
     0.3320494E+01 I  X X XX XXXXXX X XXX XXX XXX XXXXX XXX XXX X XXXXX
     0.2547007E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.1773520E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.1000033E+01 -  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1001E+04  0.2000E+04  0.3000E+04  0.4000E+04

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1956372E+02 -                                                  X
     0.1879024E+02 I
     0.1801675E+02 I
     0.1724326E+02 I
     0.1646978E+02 I
     0.1569629E+02 I
     0.1492280E+02 -
     0.1414931E+02 I
     0.1337583E+02 I
     0.1260234E+02 I
     0.1182885E+02 I
     0.1105537E+02 I                                                  X
     0.1028188E+02 -
     0.9508391E+01 I
     0.8734904E+01 I                                                  X
     0.7961417E+01 I                                                  X
     0.7187930E+01 I
     0.6414443E+01 I                                                  X
     0.5640956E+01 -                                                  X
     0.4867469E+01 I                                                  X
     0.4093982E+01 I                                                 XX
     0.3320494E+01 I                                                 X
     0.2547007E+01 I                                              XXXX
     0.1773520E+01 I                                  XXXXXXXXXXXXX
     0.1000033E+01 -  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1001E+04  0.2000E+04  0.3000E+04  0.4000E+04

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	Tocher, The Art of Simulation, 1963, pages 14-15.
o	Hammersley and Handscomb, Monte Carlo Methods, 1964, page 36.
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 104.

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Nemo Release 3.1

parran (3)

February 23, 2025

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