I want to simulate a (very long) bus route where the buses get spread out randomly over the route over time but have a mean time between bus arrivals at my bus stop of exactly 20 minutes. To do this, I create a linear strip of time, 20 million minutes, and scatter one million buses randomly on that interval. I just multiply the output of a standard random float generator (uniform distribution over interval [0,1) ) by 20 million to generate one million arrival times randomly scattered over 20 million minutes with all points on the timeline equally likely. That way, all the times between a million bus arrivals add up to the full length 20 million minutes, averaging a twenty minute wait between buses.
What I’m wondering is if this simple procedure creates a poisson process for bus arrivals. Or would this be some other process? What would the resulting process parameters be? Would someone with a better knowledge of statistics than mine mind telling me about the statistical process that results from such a simple uniformly distributed scattering of events on a timeline? It’s an easy programming technique to use, so I’d like to make sure I’m not misunderstanding it.
Thanks.
Well, there are two sides to this:
If you take the limit of infinite minutes and infinite buses then yes, you do have the poisson process
the process you describe is close to but not quite the poisson process, because there is a little bit of bias because of the limited number of buses causes some “memory” in the process.
However, why would you want to use such a process to approximate the poisson distribution when you could just generate exponential deviates by using e.g. gsl (http://www.gnu.org/software/gsl/) to get the deviates directly?