# Poisson point process simulation with a constant population?

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Kyle Cook on 1 Apr 2016
Edited: H. Paul Keeler on 1 Oct 2018
I'm trying to run a simulation of a poisson point process with both a set lambda and a set population. The poissrand function, however, randomly gives a number of points for the population. Is there any way to set the population at a fixed value?
Here is my code currently:
lamda=1000;
npoints = poissrnd(lamda);
pproc = rand(npoints,2)*100;
plot(pproc(:, 1), pproc(:, 2), '.');

H. Paul Keeler on 29 Sep 2018
Edited: H. Paul Keeler on 1 Oct 2018
For the definition of the Poisson point process, the N has to be a Poisson random variable with its mean related to the area/size of the simulation region. This is non-negotiable. But if you fix N=n to some natural number (that is, in probability language, you condition on N=n), you then get a binomial point process.
As I remarked in another response, I recently wrote about simulating these two point processes. The binomial point process on a rectangle is detailed here here. The Poisson point process on a rectangle and on a disk.