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If you have count data with small numbers and a bunch of 0's what would be the best distribution to model this? Is Poisson good at handling data with a bunch of 0's and small number between 1 and 4?

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    $\begingroup$ Or, considering there are only 0's, 1's ....4's, give us a table. $\endgroup$ – Peter Flom Apr 7 '13 at 21:05
  • $\begingroup$ If there are only 5 possible values that your data can take on, barring extremely small sample sizes, why not use the empirical frequencies of those data? For instance, if they 50% are 0 and the rest are evenly distributed between 1-4, your model is $P(X=0) = .5$, $P(X=1) = 0.125$, $P(X=2) = 0.125$, ... $\endgroup$ – AdamO Apr 7 '13 at 21:19
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It might be Poisson, or, if there are really a LOT of zeroes, possibly zero inflated Poisson. More general options are negative binomial and zero inflated negative binomial. It's hard to tell just from what you've said, but I am guessing the NB isn't needed.

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    $\begingroup$ +1 beat me to the draw. (And better know what you're talking about as well.) $\endgroup$ – Wayne Apr 7 '13 at 20:34
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A two-part regression may apply here as well - a logistic regression that predicts whether there are zero or 1+ counts, and a second Poisson or NB regression predicting the number of non-zero counts.

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