LOGPDF Subroutine

logpdf(3f) - [M_datapac:PROBABILITY_DENSITY] compute the logistic
probability density function

   SUBROUTINE LOGPDF(X,Pdf)

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

LOGPDF(3f) computes the probability density function value for
the logistic distribution with mean = 0 and standard deviation =
pi/sqrt(3).

This distribution is defined for all X and has the probability
density function

    f(X) = exp(X)/(1+exp(X))

X     The value at which the probability density function is to
      be evaluated.

PDF   the probability density function value.

program demo_logpdf
!@(#) line plotter graph of cumulative distribution function
use M_datapac, only : logpdf, plott, label
implicit none
real,allocatable  :: x(:), y(:)
integer           :: i
   call label('logpdf')
   x=[(real(i),i=-100,100,1)]
   if(allocated(y))deallocate(y)
   allocate(y(size(x)))
   do i=1,size(x)
      call logpdf(x(i)/10.0,y(i))
   enddo
   call plott(x,y,size(x))
end program demo_logpdf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.1000000E+03 -  X
  0.9166666E+02 I  X
  0.8333334E+02 I  X
  0.7500000E+02 I  X
  0.6666667E+02 I  X
  0.5833334E+02 I  XX
  0.5000000E+02 -   XX
  0.4166667E+02 I    XXX
  0.3333334E+02 I       XXXXX
  0.2500000E+02 I           XXXXX XXX X
  0.1666667E+02 I                      X XX X X XX X
  0.8333336E+01 I                                    X X XX X XXX
  0.0000000E+00 -                                                XXX
 -0.8333328E+01 I                                    X X XX X XXX
 -0.1666666E+02 I                      X XX X X XX X
 -0.2499999E+02 I           XXXXX XXX X
 -0.3333333E+02 I       XXXXX
 -0.4166666E+02 I    XXX
 -0.5000000E+02 -   XX
 -0.5833333E+02 I  XX
 -0.6666666E+02 I  X
 -0.7500000E+02 I  X
 -0.8333333E+02 I  X
 -0.9166666E+02 I  X
 -0.1000000E+03 -  X
                   I-----------I-----------I-----------I-----------I
            0.4540E-04  0.6253E-01  0.1250E+00  0.1875E+00  0.2500E+00

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