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C Library Functions  - unicdf (3)

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NAME

unicdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] trivially compute the Uniform cumulative distribution function

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

subroutine unicdf(X,Cdf)

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

DESCRIPTION

UNICDF(3f) computes the cumulative distribution function value for the uniform (rectangular) distribution on the unit interval (0,1).

This distribution has mean = 0.5 and standard deviation = sqrt(1/12) = 0.28867513.

This distribution has the probability density function f(x) = x.

That is, this is a trivial function as the output equals the input.

INPUT ARGUMENTS

X	The value at which the cumulative distribution function is to be evaluated. X should be between 0 and 1, inclusively.

OUTPUT ARGUMENTS

CDF	the REAL cumulative distribution function value.

EXAMPLES

Sample program:

   program demo_unicdf
   !@(#) line plotter graph of function
   use M_datapac, only : unicdf, plott, label
   implicit none
   integer,parameter :: n=40
   real              :: x(0:n), y(0:n)
   integer           :: i
      call label(’unicdf’)
      x=[(real(i)/real(n),i=0,n)]
      do i=0,n
         call unicdf(x(i),y(i))
      enddo
      call plott(x,y,n+1)
   end program demo_unicdf

Result:

  The following is a plot of Y(I) (vertically) versus X(I) (horizontally)
                    I-----------I-----------I-----------I-----------I
   0.1000000E+01 -                                                  X
   0.9583333E+00 I                                                XX
   0.9166667E+00 I                                             XX
   0.8750000E+00 I                                            X
   0.8333333E+00 I                                          XX
   0.7916666E+00 I                                       XX
   0.7500000E+00 -                                      X
   0.7083333E+00 I                                    XX
   0.6666666E+00 I                                 XX
   0.6250000E+00 I                                X
   0.5833333E+00 I                              XX
   0.5416666E+00 I                           XX
   0.5000000E+00 -                          X
   0.4583333E+00 I                        XX
   0.4166666E+00 I                     XX
   0.3750000E+00 I                    X
   0.3333333E+00 I                  XX
   0.2916666E+00 I               XX
   0.2500000E+00 -              X
   0.2083333E+00 I            XX
   0.1666666E+00 I         XX
   0.1250000E+00 I        X
   0.8333331E-01 I      XX
   0.4166663E-01 I   XX
   0.0000000E+00 -  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	Johnson and Kotz, Continuous Univariate Distributions -- 2, 1970, pages 57-74.

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Nemo Release 3.1

unicdf (3)

February 23, 2025

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