C Library Functions - norcdf (3)

NAME

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

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE NORCDF(X,Cdf)

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

DESCRIPTION

NORCDF(3f) computes the cumulative distribution function value for the normal (Gaussian) distribution with mean = 0 and standard deviation = 1.
This distribution is defined for all X and has the probability density function
       f(X) = (1/sqrt(2*pi))*exp(-X*X/2)

INPUT ARGUMENTS

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

OUTPUT ARGUMENTS

CDF The cumulative distribution function value.

EXAMPLES

Sample program:

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

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 X 0.5833334E+02 I X 0.5000000E+02 - X 0.4166667E+02 I X 0.3333334E+02 I X 0.2500000E+02 I XX 0.1666667E+02 I XXXXX 0.8333336E+01 I X XX XXXXX 0.0000000E+00 - XX X X X X X XX -0.8333328E+01 I XXXXX XX X -0.1666666E+02 I XXXXX -0.2499999E+02 I XX -0.3333333E+02 I X -0.4166666E+02 I X -0.5000000E+02 - X -0.5833333E+02 I X -0.6666666E+02 I X -0.7500000E+02 I X -0.8333333E+02 I X -0.9166666E+02 I X -0.1000000E+03 - X I-----------I-----------I-----------I-----------I 0.0000E+00 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 National Bureau of Standards Applied Mathematics Series 55, 1964, page 932, Formula 26.2.17.

o Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 40-111.

Nemo Release 3.1

norcdf (3)

February 23, 2025

Generated by manServer 1.08 from 6d74292c-162d-460f-a18c-eac4f80360e0 using man macros.

o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 932, Formula 26.2.17.
o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 40-111.