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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jorma Virtamo                      VTT Information Technology
phone: +358 0 456 5612             Telecommunications
fax:   +358 0 455 0115             P.O. Box 1202
email: jorma.virtamo at vtt.fi        FIN-02044 VTT
web:   http://www.vtt.fi/tte/      Finland

```

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