caucdf Subroutine

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

   subroutine caucdf(X,Cdf)

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

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))

X   The value at which the cumulative distribution function is to
    be evaluated.

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

 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

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