Re: simulating a Poisson Forest
- Subject: [mg2889] Re: simulating a Poisson Forest
- From: jorma.virtamo at vtt.fi (Jorma Virtamo)
- Date: 4 Jan 1996 13:42:47 -0600
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: mj at wri.com
deb at Alceon.com (David E. Burmaster) wrote:
>Dear MathGroupers
>
>Does anyone know a simple algorithm to simulate a "Poisson Forest" of
>random points inside a rectangle in a plane?
>
>If each coordinate in the {x, y}-pairs is drawn from an independent Uniform
>distribution, will that create a Poisson forest?
>
Yes, it does.
If you have to create just one realization of the 2-dim Poisson process
with intensity lambda, take the number of points N to be the closest
integer to the mean m=lambda*A, where A is the area to be covered.
If you have to create several realizations remember to draw N in each
realization from the Poisson distribution with mean m. If m is a very
large number it may not matter much whether you draw N from this
distribution or whether you use the closest integer to the mean. But
if m is not so large the difference can be important.
-- Jorma Virtamo
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