C Library Functions - georan (3)

NAME

georan(3f) - [M_datapac:RANDOM] generate geometric random numbers

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.

EXAMPLES

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

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)

February 23, 2025

Generated by manServer 1.08 from 6423a59f-8ea3-4975-8d71-186161c77714 using man macros.

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).

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.