POIRAN Subroutine

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

   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(:)

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.

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.

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

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

 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

The original DATAPAC library was written by James Filliben of the
Statistical Engineering Division, National Institute of Standards
and Technology.

John Urban, 2022.05.31

CC0-1.0