- #1
flux_factor
- 3
- 0
Hello,
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!
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!