POICDF Subroutine

poicdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the Poisson
cumulative distribution function

   SUBROUTINE POICDF(X,Alamba,Cdf)

    REAL(kind=wp),intent(in)  :: X
    REAL(kind=wp),intent(in)  :: Alamba
    REAL(kind=wp),intent(out) :: Cdf

POICDF(3f) computes the cumulative distribution function value at
the precision value X for the Poisson distribution with
precision 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-- 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.

X       The value at which the cumulative distribution function is
        to be evaluated. x should be non-negative and integral-valued.
ALAMBA  The value of the tail length parameter. alamba should be
        positive. 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.

CDF    The cumulative distribution function value. For the Poisson
       distribution

Even though the input to this cumulative distribution
function subroutine for this discrete distribution should (under
normal circumstances) be a discrete integer value,
X has been specified as REAL so as to conform with the datapac
convention that all input ****data**** (as opposed to sample
size, for example) variables to 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.

program demo_poicdf
!@(#) line plotter graph of cumulative distribution function
use M_datapac, only : poicdf, plott, label
implicit none
real,allocatable :: x(:), y(:)
real             :: alamba
integer          :: i
   call label('poicdf')
   x=[(real(i),i=0,100,1)]
   if(allocated(y))deallocate(y)
   allocate(y(size(x)))
   alamba=29.5
   do i=1,size(x)
      call poicdf(X(i),Alamba,y(i))
   enddo
   call plott(x,y,size(x))
end program demo_poicdf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.1000000E+03 -                                                  X
  0.9583334E+02 I                                                  X
  0.9166666E+02 I                                                  X
  0.8750000E+02 I                                                  X
  0.8333334E+02 I                                                  X
  0.7916667E+02 I                                                  X
  0.7500000E+02 -                                                  X
  0.7083334E+02 I                                                  X
  0.6666667E+02 I                                                  X
  0.6250000E+02 I                                                  X
  0.5833334E+02 I                                                  X
  0.5416667E+02 I                                                  X
  0.5000000E+02 -                                                  X
  0.4583334E+02 I                                                  X
  0.4166667E+02 I                                                 XX
  0.3750000E+02 I                                             XXXX
  0.3333334E+02 I                                    X  X X X
  0.2916667E+02 I                       X   X  X  X
  0.2500000E+02 -        X  X X  X   X
  0.2083334E+02 I   XXX X
  0.1666667E+02 I  XX
  0.1250000E+02 I  X
  0.8333336E+01 I  X
  0.4166672E+01 I  X
  0.0000000E+00 -  X
                   I-----------I-----------I-----------I-----------I
            0.1543E-12  0.2500E+00  0.5000E+00  0.7500E+00  0.1000E+01

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