caupdf Subroutine

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

   subroutine caupdf(X,Pdf)

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

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))

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

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

The original DATAPAC library was written by James Filliben of the
Statistical Engineering Division, National Institute of Standards
and Technology.

John Urban, 2022.05.31

CC0-1.0