C Library Functions - georan (3)
NAME
georan(3f) - [M_datapac:RANDOM] generate geometric random numbers
CONTENTS
Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References
SYNOPSIS
SUBROUTINE GEORAN(N,P,Iseed,X)
INTEGER,intent(in) :: N REAL(kind=wp),intent(in) :: P INTEGER,intent(inout) :: Iseed REAL(kind=wp),intent(out) :: X(:)
DESCRIPTION
GEORAN(3f) generates a random sample of size N from the geometric distribution with REAL ’Bernoulli probability’ parameter = P.The geometric distribution used herein has mean = (1-P)/P and standard deviation = sqrt((1-P)/(P*P))). This distribution is defined for all non-negative integer X-- X = 0, 1, 2, ... .
This distribution has the probability function
f(X) = P * (1-P)**X.
The geometric distribution is the distribution of the number of failures before obtaining 1 success in an indefinite sequence of Bernoulli (0,1) trials where the probability of success in a precision trial = P.
INPUT ARGUMENTS
N The desired integer number of random numbers to be generated. ISEED An integer iseed 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. P The value of the ’Bernoulli probability’ parameter for the geometric distribution. P should be between 0.0 (exclusively) and 1.0 (exclusively).
OUTPUT ARGUMENTS
X A vector (of dimension at least N) into which the generated random sample of size N from the geometric distribution will be placed.
Sample program:
program demo_georan
use m_datapac, only : georan, plott, label, plotxt, sort
implicit none
integer,parameter :: n=4000
real :: x(n)
integer :: iseed
real :: P
call label(’georan’)
P=0.2
iseed=12345
call georan(N,P,Iseed,X)
call plotxt(x,n)
call sort(x,n,x) ! sort to show distribution
call plotxt(x,n)
end program demo_georan
Results:
THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
I-----------I-----------I-----------I-----------I
0.4500000E+02 - X
0.4312500E+02 I
0.4125000E+02 I
0.3937500E+02 I
0.3750000E+02 I X
0.3562500E+02 I
0.3375000E+02 - X
0.3187500E+02 I X
0.3000000E+02 I
0.2812500E+02 I X X
0.2625000E+02 I X X X X XX
0.2437500E+02 I X X XX X X X X
0.2250000E+02 - X X X X X
0.2062500E+02 I X X X XX X XX X X X X
0.1875000E+02 I X XX X XXX X XX X XX XX XX X XX
0.1687500E+02 I X X XX X XXXX X X XXX XX XXXXX XX XX X XXXX
0.1500000E+02 I XX X XXXXXXX X X X X XX XXXX X X X X XX
0.1312500E+02 I XXXX XXXXXX XXXXXXXXX XXXXXXX X X XXXXXXXX XXXX X
0.1125000E+02 - XXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX XX XXX XXX XX
0.9375000E+01 I XXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.7500000E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.5625000E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.3750000E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.1875000E+01 I XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.0000000E+00 - 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
0.4500000E+02 - X
0.4312500E+02 I
0.4125000E+02 I
0.3937500E+02 I
0.3750000E+02 I X
0.3562500E+02 I
0.3375000E+02 - X
0.3187500E+02 I X
0.3000000E+02 I
0.2812500E+02 I X
0.2625000E+02 I X
0.2437500E+02 I X
0.2250000E+02 - X
0.2062500E+02 I XX
0.1875000E+02 I X
0.1687500E+02 I X
0.1500000E+02 I XX
0.1312500E+02 I XX
0.1125000E+02 - XX
0.9375000E+01 I XXX
0.7500000E+01 I XXXXXX
0.5625000E+01 I XXXXXX
0.3750000E+01 I XXXXXXXXXX
0.1875000E+01 I XXXXXXXXXXXXXX
0.0000000E+00 - XXXXXXXXXXX
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 Feller, An Introduction to Probability Theory and its Applications, Volume 1, Edition 2, 1957, pages 155-157, 210. o National Bureau of Standards Applied Mathematics Series 55, 1964, page 929.
| Nemo Release 3.1 | georan (3) | July 22, 2023 |
