# Approximate a poisson binomial distribution with a binomial distribution?

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.

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See this thread: stats.stackexchange.com/questions/5347/… –  onestop Jan 21 '11 at 16:05
The answer depends, in an essential manner, on precisely how your observations depart from independence and how they fail to be identically distributed. In general the binomial distribution, with a single parameter, is too "rigid" to model your sum: you should be looking at families with more parameters to allow for under- or over-dispersion. Perhaps you could tell us more about these data? –  whuber Jan 21 '11 at 17:31