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C Library Functions  - poiran (3)

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NAME

poiran(3f) - [M_datapac:RANDOM] generate Poisson random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE POIRAN(N,Alamba,Iseed,X)

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

DESCRIPTION

POIRAN(3f) generates a random sample of size N from the Poisson distribution with REAL tail length parameter = ALAMBA.

The Poisson distribution used herein has mean = ALAMBA and standard deviation = sqrt(ALAMBA).

This distribution is defined for all discrete non-negative integer X where X = 0, 1, 2, ... .

This distribution has the probability function

       f(X) = exp(-ALAMBA) * ALAMBA**X / X!

The Poisson distribution is the distribution of the number of events in the interval (0,ALAMBA) when the waiting time between events is exponentially distributed with mean = 1 and standard deviation = 1.

Note that even though the output from this discrete random number generator must necessarily be a sequence of ***integer*** values, the output vector X is REAL in mode.

X has been specified as REAL so as to conform with the DATAPAC convention that all output vectors from all DATAPAC subroutines

are REAL.
	this convention is based on the belief that

1.	A mixture of modes (floating point versus integer) is inconsistent and an unnecessary complication in a data analysis; and
2.	Floating point machine arithmetic (as opposed to integer arithmetic) is the more natural mode for doing data analysis.

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.

ALAMBA The value of the tail length parameter. Note the tail length parameter ALAMBA is not restricted to only integer values. ALAMBA can be set to any positive real value--integer or non-integer.

OUTPUT ARGUMENTS

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

EXAMPLES

Sample program:

   program demo_poiran
   use m_datapac, only : poiran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=500
   real :: x(n)
   integer :: iseed
   real :: alamba
      call label(’poiran’)
      alamba=2.0
      iseed=12345
      call poiran(N,Alamba,Iseed,X)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_poiran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.7000000E+01 -                                 X
     0.6708333E+01 I
     0.6416667E+01 I
     0.6125000E+01 I        X         XX       X      X   X          X
     0.5833333E+01 I
     0.5541667E+01 I
     0.5250000E+01 -
     0.4958333E+01 I         XX   XXXX   X  X X  X   X     XX    X
     0.4666667E+01 I
     0.4375000E+01 I
     0.4083333E+01 I  XXXX   XXX X XXXXXXX  XX XXXX  XXXXXX  X X XX XX
     0.3791667E+01 I
     0.3500000E+01 -
     0.3208333E+01 I
     0.2916667E+01 I  XXX XXXXXX X   XX XX  XXX  XXXXXXXXXXX X XXXXXXX
     0.2625000E+01 I
     0.2333333E+01 I
     0.2041667E+01 I  XXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXX XXXXXXXXXXXXXX
     0.1750000E+01 -
     0.1458333E+01 I
     0.1166667E+01 I
     0.8750000E+00 I   XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.5833335E+00 I
     0.2916670E+00 I
     0.0000000E+00 -  XXXXXXXXXXXXXXX  XX XX XXXXXXXXXXXXX  XX XXXXXX X
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1258E+03  0.2505E+03  0.3752E+03  0.5000E+03

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.7000000E+01 -                                                  X
     0.6708333E+01 I
     0.6416667E+01 I
     0.6125000E+01 I                                                 XX
     0.5833333E+01 I
     0.5541667E+01 I
     0.5250000E+01 -
     0.4958333E+01 I                                                XX
     0.4666667E+01 I
     0.4375000E+01 I
     0.4083333E+01 I                                            XXXX
     0.3791667E+01 I
     0.3500000E+01 -
     0.3208333E+01 I
     0.2916667E+01 I                                    XXXXXXXXX
     0.2625000E+01 I
     0.2333333E+01 I
     0.2041667E+01 I                        XXXXXXXXXXXXX
     0.1750000E+01 -
     0.1458333E+01 I
     0.1166667E+01 I
     0.8750000E+00 I         XXXXXXXXXXXXXXXX
     0.5833335E+00 I
     0.2916670E+00 I
     0.0000000E+00 -  XXXXXXXX

                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1258E+03  0.2505E+03  0.3752E+03  0.5000E+03

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	Cox and Miller, The Theory of Stochastic Processes, 1965, page 7.
o	Tocher, The Art of Simulation, 1963, pages 36-37.
o	Johnson and Kotz, Discrete Distributions, 1969, pages 87-121.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 108-113.
o	Feller, An Introduction to Probability Theory and Its Applications, Volume 1, Edition 2, 1957, pages 146-154.
o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 929.

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Nemo Release 3.1

poiran (3)

July 22, 2023

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