C Library Functions - lgncdf (3)

NAME

lgncdf(3f) - [M_datapac:CUMULATIVE_DISTRIBUTION] compute the lognormal cumulative distribution function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LGNCDF(X,Cdf)

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

DESCRIPTION

LGNCDF(3f) computes the cumulative distribution function value for the lognormal distribution.
The lognormal distribution used herein has mean = sqrt(e) = 1.64872127 and standard deviation = sqrt(e*(e-1)) = 2.16119742. this distribution is defined for all positive X and has the probability density function
       f(X) = (1/(X*sqrt(2*pi))) * exp(-log(X)*log(X)/2)
The lognormal distribution used herein is the distribution of the variate X = exp(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 positive.

OUTPUT ARGUMENTS

Cdf The cumulative distribution function value for the lognormal distribution

EXAMPLES

Sample program:

   program demo_lgncdf
   !@(#) line plotter graph of cumulative distribution function
   use M_datapac, only : lgncdf, plott, label
   implicit none
   real,allocatable  :: x(:), y(:)
   integer           :: i
      call label(’lgncdf’)
      x=[((real(i)+epsilon(0.0))/10.0,i=0,100,1)]
      if(allocated(y))deallocate(y)
      allocate(y(size(x)))
      do i=1,size(x)
         call lgncdf(x(i),y(i))
      enddo
      call plott(x,y,size(x))
   end program demo_lgncdf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.1000000E+02 - X 0.9583333E+01 I X 0.9166667E+01 I X 0.8750000E+01 I X 0.8333333E+01 I X 0.7916667E+01 I X 0.7500000E+01 - XX 0.7083333E+01 I X 0.6666667E+01 I X 0.6250000E+01 I X 0.5833333E+01 I X 0.5416667E+01 I X 0.5000000E+01 - X 0.4583333E+01 I XX 0.4166667E+01 I XX 0.3750000E+01 I X 0.3333333E+01 I X 0.2916667E+01 I XX 0.2500000E+01 - XXX 0.2083333E+01 I XXX 0.1666667E+01 I XXXX 0.1250000E+01 I X XX X 0.8333340E+00 I X X X X 0.4166670E+00 I X X X X 0.1192093E-07 - XX X I-----------I-----------I-----------I-----------I 0.0000E+00 0.2473E+00 0.4947E+00 0.7420E+00 0.9893E+00

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 112-136.

o Cramer, Mathematical Methods of Statistics, 1946, pages 219-220.

Nemo Release 3.1

lgncdf (3)

July 22, 2023

Generated by manServer 1.08 from c62a4578-22fd-4117-a73e-672cbb915097 using man macros.

o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 112-136.
o	Cramer, Mathematical Methods of Statistics, 1946, pages 219-220.