Poisson point process simulation with a constant population?

Question

Kyle Cook 2016-4-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/276500-poisson-point-process-simulation-with-a-constant-population

编辑： H. Paul Keeler 2018-10-1

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), '.');

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

H. Paul Keeler 2018-9-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/276500-poisson-point-process-simulation-with-a-constant-population#answer_339041

编辑：H. Paul Keeler 2018-10-1

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.