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C Library Functions  - logppf (3)

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NAME

logppf(3f) - [M_datapac:PERCENT_POINT] compute the logistic percent point function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LOGPPF(P,Ppf)

       REAL(kind=wp),intent(in)  :: P
       REAL(kind=wp),intent(out) :: Ppf

DESCRIPTION

LOGPPF(3f) computes the percent point 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))

Note that the percent point function of a distribution is identically the same as the inverse cumulative distribution function of the distribution.

INPUT ARGUMENTS

P	The value at which the percent point function is to be evaluated. P should be between 0.0 and 1.0, exclusively.

OUTPUT ARGUMENTS

PPF	The percent point function value.

EXAMPLES

Sample program:

   program demo_logppf
   use M_datapac, only : logppf, plott, label
   implicit none
   integer,parameter :: n=40
   real              :: x(n), y(n)
   integer           :: i
      call label(’logppf’)
      x=[(real(i)/real(n+1),i=1,n)]
      do i=1,n
         call logppf(x(i),y(i))
      enddo
      call plott(x,y,n)
   end program demo_logppf

Results:

    The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                      I-----------I-----------I-----------I-----------I
     0.9756098E+00 -                                                  X
     0.9359756E+00 I                                           X X
     0.8963415E+00 I                                       XX
     0.8567073E+00 I                                     X
     0.8170732E+00 I                                   XX
     0.7774390E+00 I                                  X
     0.7378049E+00 -                                 X
     0.6981707E+00 I                               XX
     0.6585366E+00 I                              X
     0.6189024E+00 I                             XX
     0.5792683E+00 I                            X
     0.5396341E+00 I                           X
     0.5000000E+00 -                          X
     0.4603658E+00 I                         X
     0.4207317E+00 I                        X
     0.3810976E+00 I                      XX
     0.3414634E+00 I                      X
     0.3018292E+00 I                    XX
     0.2621951E+00 -                   X
     0.2225609E+00 I                  X
     0.1829268E+00 I                XX
     0.1432927E+00 I               X
     0.1036585E+00 I            XX
     0.6402433E-01 I       X X
     0.2439024E-01 -  X
                      I-----------I-----------I-----------I-----------I
              -0.3689E+01 -0.1844E+01  0.4768E-06  0.1844E+01  0.3689E+01

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	Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 229-231.
o	Filliben, ’The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.
o	Johnson and Kotz, Continuous Univariate Distributions--2, 1970, pages 1-21.

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Nemo Release 3.1

logppf (3)

February 23, 2025

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