How do I generate a Poisson Process?

Question

Original Question:

I want to generate a Poisson process. If the number of arrivals by time t is N(t) and I have a Poisson distribution with parameter

Answer 1

I would be very careful about using the inverse CDF and pumping a uniform random number through it. The problem here is that often the inverse CDF is numerically unstable or the functions to produce it can give undesirable fluctuations near the ends of the interval. For that reason I would recommend something like the rejection method used in "Numerical Recipes in C". See the poidev function given in ch 7.3 of NRC: http://www.nrbook.com/a/bookcpdf/c7-3.pdf