Poisson point process simulation with a constant population?

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), '.');

Answer 1

[H. Paul Keeler]

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.