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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.

QuantIbex
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bayerj
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    See this thread: http://stats.stackexchange.com/questions/5347/how-can-i-efficiently-model-the-sum-of-bernoulli-random-variables – onestop Jan 21 '11 at 16:05
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    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

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