C Library Functions - hfncdf (3)

NAME

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

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE HFNCDF(X,Cdf)

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

DESCRIPTION

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.

INPUT ARGUMENTS

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

OUTPUT ARGUMENTS

CDF The cumulative distribution function value. for the halfnormal distribution

EXAMPLES

Sample program:

   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

Results:

    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

================================================================================

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 53, 59, 81, 83.

o Daniel, ’Use of Half-Normal Plots in Interpreting Factorial Two-level Experiments’, Technometrics, 1959, pages 311-341.

Nemo Release 3.1

hfncdf (3)

February 23, 2025

Generated by manServer 1.08 from f6bc86c6-2964-4230-bf19-ee6663f69e15 using man macros.

o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 53, 59, 81, 83.
o	Daniel, ’Use of Half-Normal Plots in Interpreting Factorial Two-level Experiments’, Technometrics, 1959, pages 311-341.