In a part of my research, I am fitting probability distribution models for the count data(and binomial data) using Poisson, Binomial, Negative Binomial and Beta Binomial models. I have few data sets in which the observed frequency and hence the expected modeled frequencies are too small(less than 5).. I want to compare the goodness of fits using a proper method. I know, Pearson's Chi-Square test will not be applicable for my purposes as it has some limitations on expected counts.
Here is a similar situation which I also deal with..
I am looking for an alternative Goodness of fit test measure which can be applied to this kind of situations.
Any suggestion is greatly appreciated.. Thank you.