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This is my first post - so let me know if I communicate incorrectly.

To start, note that my thread title may be misleading as to my actual problem. I think it describes my situation, but let me provide background and then restate my problem as I see it, so as to allow for a potentially different interpretation:

I have data that are integer frequency counts for J possibly-dependent populations over a common timeframe.

For each population, I currently assume observations are a sample from a Poisson-distributed random variable (I may allow different populations to follow different distributions such as a Negative Binomial in the future, but I'm only asking about the all-Poisson case in this post).

Main question:I want to find the CDF of the following random variable: one of the Poisson r.v.s divided by {the sum of all J Poisson r.v.'s divided by J}. I would type this in Latex, but I'm having real trouble getting it to show up correctly on the forum, even when referring to

https://www.physicsforums.com/showthread.php?t=8997

I think I can combine the individual moment generating functions and then take the inverse Laplace transformation to find the CDF? Is there another way (is there a simple analytical solution that I'm overlooking)?

Does the problem simplify if the random variables are assumed independent?

Thank you very much!

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# CDF of the ratio of Poisson and possibly-Poisson R.V.

Can you offer guidance or do you also need help?

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