I have samples of Bernoulli distributed variable that are neither the first nor the second i in iid. My goal is to model their sum.
I got from Wikipedia that I can use the poisson binomial distribution to make up for one of the i's, but then I have to keep all the inidividual probabilities.
It would probably also be possible to throw the central limit theorem against it somehow to model it as a Gaussian, but I wonder if I can do better.
Are there any results on how well a binomial distribution fits the sum of non identically non independently distributed Bernoulli samples. Especially if I can get some bounds on the accuracy wrt the correlation of the samples or something like that.