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Hello StackExchange users,

I am trying to figure out how do I simulate a time dependent Poisson process through N(t). However, my main problem is having trouble understanding what N is and how to go about simulating it. I know my time parameter, t, and I know the lambda parameter that the Poisson distribution is dependent upon. Is there anyone willing to give me some help or lead me in the right direction?

By bypassing exponential waiting times I plan to take this N simulation and simulate uniform numbers numbers and re-roder them. But I need to be able to simulate N(t) first.

Thank You

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If $\{N(t)\}$ is a Poisson process then $N(t) \sim Po(\lambda t)$. So to simulate a Poisson process you first need to draw $N \sim Po(\lambda t)$ and then you simulate $N$ uniform random numbers on the interval $[0,t]$.

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  • $\begingroup$ So let's just say lambda = 3, and t = 2. Can I simulate say 10,000 numbers from a Poisson(6) and call that N? And then simulate 10,000 uniform random numbers from [0,2]? $\endgroup$
    – user6276
    Mar 1, 2015 at 20:23
  • $\begingroup$ If you want to simulate one realization of the process you simulate one number $N$ from $Po(6)$. Then you simulate $N$ uniform random numbers from $[0,2]$. $\endgroup$
    – Lotus3000
    Mar 1, 2015 at 20:42
  • $\begingroup$ Ahhhh. So say Poisson(6) gave back 7, then I simulate 7 uniform numbers over [0,2]. That makes a lot of sense. $\endgroup$
    – user6276
    Mar 1, 2015 at 20:47

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