Dear Liu,

from your description of data, it seems you could try a mixture model for your data. A mixture model assumes that your data don't arise from a single population, but rather from a linear combination of two or more subpopulations, each one with its own distribution and weight, under the constraint that all the weights must sum up to one. In your case, you could try to fit a Poisson mixture model and check whether two components are enough or more are needed. In R there are some packages that allow you to fit mixture models with ML methods or even with Bayesian methods. I'd suggest you to look at the package "Flexmix".

Thanks so much, Fava. I will certainly try the package.