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MathGroup Archive 1996

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Re: simulating a Poisson Forest

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2889] Re: simulating a Poisson Forest
  • From: Jorma Virtamo <jorma.virtamo at vtt.fi>
  • Date: Thu, 4 Jan 1996 10:30:59 -0500

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
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email: jorma.virtamo at vtt.fi        FIN-02044 VTT                        
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