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C Library Functions  - lgnran (3)

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NAME

lgnran(3f) - [M_datapac:RANDOM] generate lognormal random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LGNRAN(N,Iseed,X)

       INTEGER,intent(in)        :: N
       INTEGER,intent(inout)     :: Iseed
       REAL(kind=wp),intent(out) :: X(:)

DESCRIPTION

LGNRAN(3f) generates a random sample of size N from the lognormal distribution.

The prototype 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 prototype 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

N	The desired integer number of random numbers to be generated.

ISEED	An integer seed value. Should be set to a non-negative value to start a new sequence of values. Will be set to -1 on return to indicate the next call should continue the current random sequence walk.

OUTPUT ARGUMENTS

X	A vector (of dimension at least N) into which the generated random sample of size N from the lognormal distribution will be placed.

EXAMPLES

Sample program:

   program demo_lgnran
   use m_datapac, only : lgnran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=500
   real :: x(n)
   integer :: iseed
      call label(’lgnran’)
      iseed=12345
      call lgnran(N,Iseed,X)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_lgnran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.2626150E+02 -                                                X
     0.2516970E+02 I
     0.2407790E+02 I
     0.2298611E+02 I
     0.2189431E+02 I
     0.2080252E+02 I
     0.1971072E+02 -
     0.1861893E+02 I
     0.1752713E+02 I   X
     0.1643533E+02 I                                               X
     0.1534354E+02 I
     0.1425174E+02 I
     0.1315995E+02 -                                        X
     0.1206815E+02 I
     0.1097635E+02 I                                    X
     0.9884558E+01 I                   X                              X
     0.8792763E+01 I                                         XXX
     0.7700968E+01 I          X
     0.6609171E+01 -                X                X      X X       X
     0.5517376E+01 I              XX   X X X        XX X        X
     0.4425579E+01 I          XX X     X X XXXX  XX X   X        XX  X
     0.3333784E+01 I   X  XXX   X  XX   XX   XXX X XXXX  X X    X  X
     0.2241987E+01 I  X XXXXXX XX  XXXX XXXXXXXXXX X XXXXXX XXX XXXXXXX
     0.1150192E+01 I  XXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
     0.5839747E-01 -  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1258E+03  0.2505E+03  0.3752E+03  0.5000E+03

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.2626150E+02 -                                                  X
     0.2516970E+02 I
     0.2407790E+02 I
     0.2298611E+02 I
     0.2189431E+02 I
     0.2080252E+02 I
     0.1971072E+02 -
     0.1861893E+02 I
     0.1752713E+02 I                                                  X
     0.1643533E+02 I                                                  X
     0.1534354E+02 I
     0.1425174E+02 I
     0.1315995E+02 -                                                  X
     0.1206815E+02 I
     0.1097635E+02 I                                                  X
     0.9884558E+01 I                                                 XX
     0.8792763E+01 I                                                 X
     0.7700968E+01 I                                                 X
     0.6609171E+01 -                                                XX
     0.5517376E+01 I                                                X
     0.4425579E+01 I                                              XX
     0.3333784E+01 I                                           XXX
     0.2241987E+01 I                                    XXXXXXXX
     0.1150192E+01 I                 XXXXXXXXXXXXXXXXXXXX
     0.5839747E-01 -  XXXXXXXXXXXXXXXX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1258E+03  0.2505E+03  0.3752E+03  0.5000E+03

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	Tocher, The Art of Simulation, 1963, pages 14-15.
o	Hammersley and Handscomb, Monte Carlo Methods, 1964, page 36.
o	Cramer, Mathematical Methods of Statistics, 1946, pages 219-220.
o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 112-136.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 88.

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Nemo Release 3.1

lgnran (3)

July 22, 2023

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