C Library Functions - lamran (3)

NAME

lamran(3f) - [M_datapac:RANDOM] generate Tukey-Lambda random numbers

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE LAMRAN(N,Alamba,Iseed,X)

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

DESCRIPTION

LAMRAN(3f) generates a random sample of size N from the (Tukey) lambda distribution with tail length parameter value = ALAMBA.
In general, the probability density function for this distribution is not simple. the percent point function for this distribution is
       g(P) = ((P**ALAMBA)-((1-P)**ALAMBA))/ALAMBA

INPUT ARGUMENTS

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

ALAMBA The value of LAMBDA (the tail length parameter).

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 (Tukey) lambda distribution will be placed.

EXAMPLES

Sample program:

   program demo_lamran
   use m_datapac, only : lamran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=400
   real :: x(n)
   integer :: iseed
   real :: gamma
      call label(’lamran’)
      gamma=3.4
      iseed=12345
      call lamran(n,gamma,iseed,x)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_lamran

Results:

THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY I-----------I-----------I-----------I-----------I 0.2940770E+00 - XX X X X 0.2701390E+00 I XXX X X X X X X 0.2462010E+00 I X XX X X X X 0.2222630E+00 I X XX X X X X X X X X 0.1983251E+00 I XX XX XX X X 0.1743871E+00 I XX X XX X X X X X X X XX XXXX 0.1504491E+00 - X X XX X X X XX X X 0.1265111E+00 I X X XXX X X X XX XX XX X X 0.1025732E+00 I X XX XXX XX XXXX XX X X XXXX 0.7863519E-01 I X XX XXXXX X X X X XXX X X XX 0.5469720E-01 I X XXX X X XX X X XX X XX X 0.3075922E-01 I X XXX X XXXX XXX XX XXX X XX XX X 0.6821245E-02 - XXXX X XX X X X X XX XX XX XX X X -0.1711673E-01 I X X X XX X XX XX X XX X X XX -0.4105473E-01 I XX X X XXXXXX XXXX XX X X X XXX -0.6499270E-01 I X XX X X X XX XXXX X XX X -0.8893067E-01 I X X X XX X X XX X X XX X X X -0.1128686E+00 I X X X X X X X X XX -0.1368066E+00 - XX X X X X X XXX X X X -0.1607446E+00 I X XX X X X X X XX X X -0.1846826E+00 I X X XX XXX X X X X X X X X X -0.2086205E+00 I X XX X X X X X XX XXX -0.2325585E+00 I X X X X X X -0.2564965E+00 I XX X X X -0.2804345E+00 - X X X X X X X I-----------I-----------I-----------I-----------I 0.1000E+01 0.1008E+03 0.2005E+03 0.3002E+03 0.4000E+03

THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY I-----------I-----------I-----------I-----------I 0.2940770E+00 - X 0.2701390E+00 I XX 0.2462010E+00 I XX 0.2222630E+00 I XX 0.1983251E+00 I XX 0.1743871E+00 I XXX 0.1504491E+00 - XXX 0.1265111E+00 I XXX 0.1025732E+00 I XXXX 0.7863519E-01 I XXXX 0.5469720E-01 I XXX 0.3075922E-01 I XXXX 0.6821245E-02 - XXXX -0.1711673E-01 I XXXX -0.4105473E-01 I XXXX -0.6499270E-01 I XXX -0.8893067E-01 I XXX -0.1128686E+00 I XX -0.1368066E+00 - XXX -0.1607446E+00 I XXX -0.1846826E+00 I XXX -0.2086205E+00 I XXX -0.2325585E+00 I X -0.2564965E+00 I X -0.2804345E+00 - XX I-----------I-----------I-----------I-----------I 0.1000E+01 0.1008E+03 0.2005E+03 0.3002E+03 0.4000E+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 Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 53-58.

o Filliben, ’The Percent Point Function’, (unpublished manuscript), 1970, pages 28-31.

Nemo Release 3.1

lamran (3)

July 22, 2023

Generated by manServer 1.08 from 1c5d4d62-b05c-440e-a33c-2516364c0293 using man macros.

N	The desired integer number of random numbers to be generated.
ALAMBA	The value of LAMBDA (the tail length parameter).
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.

o	Tocher, The Art of Simulation, 1963, pages 14-15.
o	Hammersley and Handscomb, Monte Carlo Methods, 1964, page 36.
o	Filliben, Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution (Unpublished PH.D. Dissertation, Princeton University), 1969, pages 21-44, 53-58.
o	Filliben, ’The Percent Point Function’, (unpublished manuscript), 1970, pages 28-31.