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C Library Functions  - cauran (3)

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NAME

cauran(3f) - [M_datapac:RANDOM] generate Cauchy random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE CAURAN(N,Iseed,X)

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

DESCRIPTION

CAURAN(3f) generates a random sample of size N from the Cauchy distribution with median = 0 and 75% point = 1.

This distribution is defined for all X and has the probability density function

       f(X) = (1/pi)*(1/(1+X*X))

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 function value for the Cauchy distribution will be placed.

EXAMPLES

Sample program:

   program demo_cauran
   use m_datapac, only : cauran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=100
   real              :: x(n)
   integer           :: iseed
      call label(’cauran’)
      iseed=12345
      call cauran(n,iseed,x)
      write(*,*)x
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_cauran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.8386762E+02 -                                                 X
     0.7943768E+02 I
     0.7500773E+02 I
     0.7057778E+02 I
     0.6614783E+02 I
     0.6171789E+02 I
     0.5728794E+02 -
     0.5285799E+02 I
     0.4842804E+02 I
     0.4399810E+02 I
     0.3956815E+02 I
     0.3513820E+02 I
     0.3070825E+02 -
     0.2627831E+02 I
     0.2184836E+02 I
     0.1741841E+02 I
     0.1298846E+02 I     X    X
     0.8558517E+01 I            X  X                   X
     0.4128571E+01 -                X X X  X        X   X      XX XX
    -0.3013763E+00 I  XXX XXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXX
    -0.4731323E+01 I  XX       X  X  X   X   XX      X     X
    -0.9161270E+01 I
    -0.1359122E+02 I       X
    -0.1802116E+02 I
    -0.2245111E+02 -     X                            X      X
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.2575E+02  0.5050E+02  0.7525E+02  0.1000E+03

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.8386762E+02 -                                                  X
     0.7943768E+02 I
     0.7500773E+02 I
     0.7057778E+02 I
     0.6614783E+02 I
     0.6171789E+02 I
     0.5728794E+02 -
     0.5285799E+02 I
     0.4842804E+02 I
     0.4399810E+02 I
     0.3956815E+02 I
     0.3513820E+02 I
     0.3070825E+02 -
     0.2627831E+02 I
     0.2184836E+02 I
     0.1741841E+02 I
     0.1298846E+02 I                                                 XX
     0.8558517E+01 I                                                XX
     0.4128571E+01 -                                           XXXXX
    -0.3013763E+00 I         XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
    -0.4731323E+01 I    XXXXXX
    -0.9161270E+01 I
    -0.1359122E+02 I   X
    -0.1802116E+02 I
    -0.2245111E+02 -  XX
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.2575E+02  0.5050E+02  0.7525E+02  0.1000E+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, page 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, page 231.
o	Filliben, ’The Percent Point Function’, (Unpublished Manuscript), 1970, pages 28-31.
o	Johnson and Kotz, Continuous Univariate Distributions--1, 1970, pages 154-165.

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Nemo Release 3.1

cauran (3)

February 23, 2025

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