Working with cross-sectional
insurance data, Boucher et al. (2007) sustain that the comparison of the log-likelihoods for
the two distributions reveals that the extra parameter of the negative binomial distribution
improves the fit of data in comparison with the Poisson distribution. For longitudinal or
panel data, an excellent account of claim frequency distributions can be consulted in
Boucher et al. (2008), Boucher and Guillen (2009) and Antonio and Valdez (2010), in
which the authors analyse and emphasize the practical use of negative binomial models for
auto insurance data.