C Library Functions - ev1ran (3)

NAME

ev1ran(3f) - [M_datapac:RANDOM] generate extreme value type 1 (Gumbel) random numbers

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE EV1RAN(N,Iseed,X)

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

DESCRIPTION

EV1RAN(3f) generates a random sample of size N from the extreme value type 1 distribution.
The prototype extreme value type 1 distribution used herein has mean = Euler’s number = 0.57721566 and standard deviation = pi/sqrt(6) = 1.28254983. This distribution is defined for all X and has the probability density function
       f(X) = (exp(-X)) * (exp(-(exp(-X))))

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.

OUTPUT ARGUMENTS

X A vector (of dimension at least N) into which the generated random sample of size N from the extreme value type 1 distribution will be placed.

EXAMPLES

Sample program:

   program demo_ev1ran
   use m_datapac, only : ev1ran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=4000
   real :: x(n)
   integer :: iseed
      call label(’ev1ran’)
      iseed=12345
      call ev1ran(n,iseed,x)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_ev1ran

Results:

THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY I-----------I-----------I-----------I-----------I 0.1011052E+02 - X 0.9597239E+01 I 0.9083955E+01 I 0.8570670E+01 I 0.8057385E+01 I X 0.7544101E+01 I X 0.7030817E+01 - X 0.6517532E+01 I X X 0.6004248E+01 I X X X X XX 0.5490964E+01 I X X XX X X X X X 0.4977679E+01 I X X X X X XXX X X X X 0.4464395E+01 I X X XXX X XX X X X XX X X 0.3951111E+01 - X X XX XXXXXX X X XXX XXX XXXXX XXX XXX X XXXXX 0.3437826E+01 I XXXXXXXXXXXXXX XXXXXXXX XX XX XXXX X X XX XXXXXX 0.2924542E+01 I XXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXX 0.2411257E+01 I XXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXX XXXXXXXXXXXXX 0.1897973E+01 I XXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX 0.1384688E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 0.8714046E+00 - XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 0.3581200E+00 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.1551647E+00 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.6684484E+00 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.1181733E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX -0.1695018E+01 I X XXX XX XXXXXXXXXXXXXXXXXXXXXXX X X XXXXX -0.2208302E+01 - X X 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 272-295.

Nemo Release 3.1

ev1ran (3)

July 22, 2023

Generated by manServer 1.08 from dc76967d-0b71-45ea-8076-f8bc53930575 using man macros.

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.

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.