hfncdf Subroutine

hfncdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the half-normal cumulative
distribution function

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

HFNCDF(3f) computes the cumulative distribution function value for
the halfnormal distribution.

The halfnormal distribution used herein has mean = sqrt(2/pi) =
0.79788456 and standard deviation = 1.

This distribution is defined for all non-negative x and has the
probability density function

f(X) = (2/sqrt(2*pi)) * exp(-X*X/2).

The halfnormal distribution used herein is the distribution of the
variate X = abs(z) where the variate z is normally distributed with
mean = 0 and standard deviation = 1.

X     The value at which the cumulative distribution function is
      to be evaluated.  X should be non-negative.

CDF   The cumulative distribution function value.
      for the halfnormal distribution

program demo_hfncdf
!@(#) line plotter graph of cumulative distribution function
!@(#) for the halfnormal distribution
use M_datapac, only : hfncdf, plott, label
implicit none
real,allocatable  :: x(:), y(:)
integer           :: i
   call label('hfncdf')
   x=[(real(i),i=0,100,1)]
   if(allocated(y))deallocate(y)
   allocate(y(size(x)))
   do i=1,size(x)
      call hfncdf(x(i)/10.0,y(i))
   enddo
   call plott(x,y,size(x))
end program demo_hfncdf

 The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                   I-----------I-----------I-----------I-----------I
  0.1000000E+03 -                                                  X
  0.9583334E+02 I                                                  X
  0.9166666E+02 I                                                  X
  0.8750000E+02 I                                                  X
  0.8333334E+02 I                                                  X
  0.7916667E+02 I                                                  X
  0.7500000E+02 -                                                  X
  0.7083334E+02 I                                                  X
  0.6666667E+02 I                                                  X
  0.6250000E+02 I                                                  X
  0.5833334E+02 I                                                  X
  0.5416667E+02 I                                                  X
  0.5000000E+02 -                                                  X
  0.4583334E+02 I                                                  X
  0.4166667E+02 I                                                  X
  0.3750000E+02 I                                                  X
  0.3333334E+02 I                                                  X
  0.2916667E+02 I                                                  X
  0.2500000E+02 -                                                 XX
  0.2083334E+02 I                                               XXX
  0.1666667E+02 I                                            XXXX
  0.1250000E+02 I                                     X X XX
  0.8333336E+01 I                           X  X X  X
  0.4166672E+01 I             X   X  X   X
  0.0000000E+00 -  X   X   X
                   I-----------I-----------I-----------I-----------I
           -0.1192E-06  0.2500E+00  0.5000E+00  0.7500E+00  0.1000E+01

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