NetNews Usenet Archive 1992 #18/NN_1992_18.iso/spool/sci/math/stat/1669

Text File | 1992-08-16 | 1.6 KB | 38 lines

Newsgroups: sci.math.stat
Path: sparky!uunet!elroy.jpl.nasa.gov!usc!sol.ctr.columbia.edu!destroyer!ubc-cs!fs1.ee.ubc.ca!victorw
From: [e-mail] (Victor J. K. Wong)
Subject: simulation of 2-dimensional Poisson distribution
Message-ID: <[e-mail]>
Sender: [e-mail] (Victor J. K. Wong)
Organization: University of BC, Electrical Engineering
Date: Sun, 16 Aug 1992 23:48:29 GMT
Lines: 27


Hi reader,

For a 2-dimensional homogenous Poisson distribution,
p(i,A) = exp(-A*d)*(A*d)^i/i! where p(i,A) is the probability
of i occurrences in an area A, d is the spatial density
(number of occurrences per unit area). Similar to the
one-dimensional Poisson distribution, 2-dimensional one
also has the memoryless property.

To simulate a 2-dimensional Poisson environemnt, one can
divide an area A into many small areas with equal size B.
If B is small enough, p(0,B) + p(1,B) is very close to 1
and hence, p(i,B), for i > 1, can be discarded. For each
small area B, the probability of occurrence is p(1,B) and
the probability of no occurrence is p(0,B), and this is
a binominal process. If B is very small, one can assume
that the location of the occurrence is the center of the
area B If this process repeats for each area B, the
distribution of of any area in A is a 2-dimensional
Poisson. However, such a simulation takes long time, does
anyone has better suggestion for a faster simulation of
a 2-dimensional Poisson environment? If you have any
suggestion, please email to me (email address [e-mail]).
Your help will be very much appreciated.

Victor