Abstract: Poisson and negative binomial distributions are usually used to fit claim frequencies. The two discrete distributions and binomial distribution totally constitute a class of discrete non-negative integer-valued distributions called (a,b,0) family. In this paper, we discuss (a,b,0) family first. Then we advance a hypothesis testing method to distinguish which distribution it is from when given a set of claim frequency data. In section 3, we apply the method on real claim frequency data from some domestic insurer and make a simulative study on the power of the method.