According to the literature, mixed results were obtained concerning the models employed to estimate the claim frequency. In the application of Cameron and Trived (1998), the NB2 model is preferred to NB1 as it has higher log-likelihood, with the same number of parameters. In contrary, the results of a more recent study of Boucher et al. (2007) confirm that the NB1 was one of the best models to fit the auto insurance data with which they worked. Analysing different type of insurance data, including auto portfolios, Hilbe (2014) argues that NB1 and NB2 are valuable models both to diagnose and to adjust overdispersion in data. Hence, there is no empirical evidence in the literature to support a certain count model, given the fact that the overdispersion appears for several reasons as discussed previous in this section.