both statistics presented in this paper reach the same conclusion, meaning the existence of overdispersion within the studied insurance portfolio. Results of these tests showed that NB models correct the overdispersion, providing a better fit to the data in comparison to the Poisson model. Furthermore, the comparison of NB1 and NB2 models indicated that the last one is preferred. By using the likelihood ratio in order to test the fit of the NB2 model, the results suggest that this model is the most appropriate to deal with the problem of overdispersion and to predict the claim frequency for the analyzed auto insurance portfolio.