C Library Functions - lgnppf (3)

NAME

lgnppf(3f) - [M_datapac:PERCENT_POINT] compute the lognormal percent point function

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LGNPPF(P,Ppf)

       REAL(kind=wp),intent(in)  :: P
       REAL(kind=wp),intent(out) :: Ppf

DESCRIPTION

LGNPPF(3f) computes the percent point 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.
Note that the percent point function of a distribution is identically the same as the inverse cumulative distribution function of the distribution.

INPUT ARGUMENTS

P The value (between 0.0 (exclusively) and 1.0 (exclusively)) at which the percent point function is to be evaluated.

OUTPUT ARGUMENTS

PPF The percent point function value for the lognormal distribution

EXAMPLES

Sample program:

   program demo_lgnppf
   !@(#) line plotter graph of function
   use M_datapac, only : lgnppf, plott, label
   implicit none
   integer,parameter :: n=200
   real              :: x(n), y(n)
   integer           :: i
      call label(’lgnppf’)
      x=[(real(i)/real(n+1),i=1,n)]
      do i=1,n
         call lgnppf(x(i),y(i))
      enddo
      call plott(x,y,n)
   end program demo_lgnppf

Results:

The following is a plot of Y(I) (vertically) versus X(I) (horizontally) I-----------I-----------I-----------I-----------I 0.9950249E+00 - X X X X X 0.9537728E+00 I XXXXXXX X 0.9125207E+00 I XXXX 0.8712686E+00 I XXX 0.8300166E+00 I XX 0.7887645E+00 I XX 0.7475125E+00 - X 0.7062603E+00 I X 0.6650083E+00 I XX 0.6237562E+00 I X 0.5825042E+00 I X 0.5412520E+00 I X 0.5000000E+00 - XX 0.4587479E+00 I X 0.4174958E+00 I X 0.3762438E+00 I XX 0.3349917E+00 I X 0.2937396E+00 I X 0.2524875E+00 - XX 0.2112355E+00 I X 0.1699834E+00 I X 0.1287313E+00 I X 0.8747923E-01 I X 0.4622716E-01 I XX 0.4975124E-02 - X I-----------I-----------I-----------I-----------I 0.7596E-01 0.3348E+01 0.6620E+01 0.9893E+01 0.1316E+02

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

lgnppf (3)

July 22, 2023

Generated by manServer 1.08 from 461c8fe0-5cd4-4bf5-84bf-82cf5174ddd4 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.