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C Library Functions  - logpdf (3)

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NAME

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

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LOGPDF(X,Pdf)

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

DESCRIPTION

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))

INPUT ARGUMENTS

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

OUTPUT ARGUMENTS

PDF	the probability density function value.

EXAMPLES

Sample program:

   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

Results:

    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

Results:

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	Johnson and Kotz, Continuous Univariate Distributions--2, 1970, pages 1-21.

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Nemo Release 3.1

logpdf (3)

July 22, 2023

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