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C Library Functions  - caupdf (3)

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NAME

caupdf(3f) - [M_datapac:PROBABILITY_DENSITY] compute the Cauchy probability density function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

subroutine caupdf(X,Pdf)

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

DESCRIPTION

CAUPDF(3f) computes the probability density 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 probability density function is to be evaluated.

OUTPUT ARGUMENTS

PDF	The probability density function value.

EXAMPLES

Sample program:

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

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  XX
     0.5833334E+02 I   X
     0.5000000E+02 -   XX
     0.4166667E+02 I    XX
     0.3333334E+02 I     XX
     0.2500000E+02 I       XXXX
     0.1666667E+02 I           XXXXXX X X
     0.8333336E+01 I                     X X  X X  X  X  X  X
     0.0000000E+00 -                                           X  X X X
    -0.8333328E+01 I                     X X  X X  X  X  X  X
    -0.1666666E+02 I           XXXXXX X X
    -0.2499999E+02 I       XXXX
    -0.3333333E+02 I     XX
    -0.4166666E+02 I    XX
    -0.5000000E+02 -   XX
    -0.5833333E+02 I   X
    -0.6666666E+02 I  XX
    -0.7500000E+02 I  X
    -0.8333333E+02 I  X
    -0.9166666E+02 I  X
    -0.1000000E+03 -  X
                      I-----------I-----------I-----------I-----------I
               0.3152E-02  0.8194E-01  0.1607E+00  0.2395E+00  0.3183E+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

caupdf (3)

February 23, 2025

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