C Library Functions - ev2ran (3)
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.
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_ev2ranResults:
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+04THE 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.
| Nemo Release 3.1 | ev2ran (3) | July 22, 2023 |
