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C Library Functions  - ev2ran (3)

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NAME

ev2ran(3f) - [M_datapac:RANDOM] generate extreme value type 2 (Frechet) random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE EV2RAN(N,Gamma,Iseed,X)

       INTEGER,intent(in)        :: N
       INTEGER,intent(inout)     :: Iseed
       REAL(kind=wp),intent(in)  :: Gamma
       REAL(kind=wp),intent(out) :: X(:)

DESCRIPTION

EV2RAN(3f) generates a random sample of size N from the extreme value type 2 distribution with tail length parameter value = GAMMA.

The prototype extreme value type 2 distribution used herein is defined for all non-negative X, and has the probability density function

       f(X) = GAMMA * (X**(-GAMMA-1)) * exp(-(X**(-GAMMA)))

INPUT ARGUMENTS

N	The desired integer number of random numbers to be generated.
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.
GAMMA	The value of the tail length parameter. GAMMA should be positive.

OUTPUT ARGUMENTS

X	A vector (of dimension at least N) into which the generated random sample of size N from the extreme value type 2 distribution will be placed.

EXAMPLES

Sample program:

   program demo_ev2ran
   use m_datapac, only : ev2ran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=8000
   real :: x(n)
   integer :: iseed
   real :: gamma
      call label(’ev2ran’)
      gamma=3.4
      iseed=12345
      call ev2ran(N,Gamma,Iseed,X)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_ev2ran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1956361E+02 -   X
     0.1876934E+02 I
     0.1797507E+02 I
     0.1718080E+02 I
     0.1638653E+02 I
     0.1559226E+02 I                                   X
     0.1479799E+02 -
     0.1400372E+02 I
     0.1320944E+02 I
     0.1241517E+02 I
     0.1162090E+02 I          X
     0.1082663E+02 I                                               X
     0.1003236E+02 -
     0.9238092E+01 I              X               X
     0.8443822E+01 I
     0.7649551E+01 I                   X                             X
     0.6855281E+01 I          X          X             X
     0.6061010E+01 I       X   X    X   X X                    X    X
     0.5266740E+01 -   X     XXX    XX    X      X   X X       X  X  X
     0.4472469E+01 I   XX  XX     X XX X XXX XX  X  XX X     X X X X X
     0.3678199E+01 I   XX X  XXX XXXXX XX XX XX XX XXXX  XXXXXXX XXXXXX
     0.2883928E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.2089659E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.1295387E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.5011185E+00 -  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.2001E+04  0.4000E+04  0.6000E+04  0.8000E+04

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1956361E+02 -                                                  X
     0.1876934E+02 I
     0.1797507E+02 I
     0.1718080E+02 I
     0.1638653E+02 I
     0.1559226E+02 I                                                  X
     0.1479799E+02 -
     0.1400372E+02 I
     0.1320944E+02 I
     0.1241517E+02 I
     0.1162090E+02 I                                                  X
     0.1082663E+02 I                                                  X
     0.1003236E+02 -
     0.9238092E+01 I                                                  X
     0.8443822E+01 I
     0.7649551E+01 I                                                  X
     0.6855281E+01 I                                                  X
     0.6061010E+01 I                                                  X
     0.5266740E+01 -                                                  X
     0.4472469E+01 I                                                  X
     0.3678199E+01 I                                                 XX
     0.2883928E+01 I                                                XX
     0.2089659E+01 I                                           XXXXXX
     0.1295387E+01 I             XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.5011185E+00 -  XXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.2001E+04  0.4000E+04  0.6000E+04  0.8000E+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 272-295.

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Nemo Release 3.1

ev2ran (3)

February 23, 2025

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