# Best distribution for rare data

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?

• Or, considering there are only 0's, 1's ....4's, give us a table. – Peter Flom Apr 7 '13 at 21:05
• 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 $P(X=0) = .5$, $P(X=1) = 0.125$, $P(X=2) = 0.125$, ... – AdamO Apr 7 '13 at 21:19