LOGCDF Subroutine

public subroutine LOGCDF(X, Cdf)

NAME

logcdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the logistic
cumulative distribution function

SYNOPSIS

   SUBROUTINE LOGCDF(X,Cdf)

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

DESCRIPTION

LOGCDF(3f) computes the cumulative distribution 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 cumulative distribution function is to
      be evaluated.

OUTPUT ARGUMENTS

CDF   The cumulative distribution function value.

EXAMPLES

Sample program:

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

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                                                  X
  0.5000000E+02 -                                                  X
  0.4166667E+02 I                                                 X
  0.3333334E+02 I                                                XX
  0.2500000E+02 I                                             XXX
  0.1666667E+02 I                                        XXXXX
  0.8333336E+01 I                                XXXXXXXX
  0.0000000E+00 -                     XX XXXXX XX
 -0.8333328E+01 I             XXXXXXXX
 -0.1666666E+02 I        XXXXX
 -0.2499999E+02 I     XXX
 -0.3333333E+02 I   XX
 -0.4166666E+02 I   X
 -0.5000000E+02 -  X
 -0.5833333E+02 I  X
 -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  0.2500E+00  0.5000E+00  0.7500E+00  0.1000E+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

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

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: X
real(kind=wp), intent(out) :: Cdf

Source Code

SUBROUTINE LOGCDF(X,Cdf)
REAL(kind=wp),intent(in) :: X
REAL(kind=wp),intent(out) :: Cdf
!
!     CHECK THE INPUT ARGUMENTS FOR ERRORS -- NO INPUT ARGUMENT ERRORS POSSIBLE FOR THIS DISTRIBUTION.
!
      IF ( X>=0.0_wp ) THEN
         Cdf = 1.0_wp/(1.0_wp+EXP(-X))
      ELSE
         Cdf = EXP(X)/(1.0_wp+EXP(X))
      ENDIF

END SUBROUTINE LOGCDF