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C Library Functions  - caucdf (3)

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NAME

caucdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the Cauchy cumulative distribution function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

subroutine caucdf(X,Cdf)

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

DESCRIPTION

CAUCDF(3f) computes the cumulative distribution function value for the Cauchy distribution with median = 0 and 75% point = 1.

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

       f(X) = (1/pi)*(1/(1+X*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_caucdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : caucdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   integer           :: i
      call label(’caucdf’)
      x=[(real(i),i=-100,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      do i=1,size(x)
         call caucdf(x(i)/10.0,y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_caucdf

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                                                 XX
     0.6666667E+02 I                                                 X
     0.5833334E+02 I                                                 X
     0.5000000E+02 -                                                XX
     0.4166667E+02 I                                               XX
     0.3333334E+02 I                                              XX
     0.2500000E+02 I                                            XXX
     0.1666667E+02 I                                         XXXX
     0.8333336E+01 I                                  XXXXXXX
     0.0000000E+00 -                    XX XX X XX XX
    -0.8333328E+01 I            XXXXXXX
    -0.1666666E+02 I        XXXX
    -0.2499999E+02 I      XXX
    -0.3333333E+02 I     XX
    -0.4166666E+02 I    XX
    -0.5000000E+02 -   XX
    -0.5833333E+02 I   X
    -0.6666666E+02 I   X
    -0.7500000E+02 I  XX
    -0.8333333E+02 I  X
    -0.9166666E+02 I  X
    -0.1000000E+03 -  X
                      I-----------I-----------I-----------I-----------I
               0.3173E-01  0.2659E+00  0.5000E+00  0.7341E+00  0.9683E+00

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 -- 1, 1970, pages 154-165.

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Nemo Release 3.1

caucdf (3)

February 23, 2025

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