Let me say that I have a sum of N random variables that follow a specific distribution. Let's say Nakagami-m. The sum can be approximated by the normal.
The problem is that, given four different probabilities, the m changes. More specifically, with P1 I sum all the N variables but all of them are following Nakagami-1, with P2 all follow Nakagami-2 etc.
If the case was just a sum of N iid random variables following a specific Nakagami-m I would approximate them by the normal. Now what do I do? It seems like X = P1Sum(Nakagami-1) + ... + P4Sum(Nakagami-4) where each sum sums N iid variables.
Thanks in advance