A Note About Model Selection and Hypothesis Test Procedure to Discriminate Poisson and Bell Models

The Bell distribution was introduced recently in the statistical literature. This distribution can be very similar to the Poisson distribution, and so it is quite important to provide procedures to discriminate these models. In this paper, we consider the Vuong test procedure and the Akaike information criterion to do that. Monte Carlo simulation experiments are carried out to study the performance of this test procedure to discriminate these two models, and comparisons with the Akaike criterion are made. An application to real data is also considered for illustrative purposes.