4. Claim frequency distribution fits
To initially understand how the different count data models fit to the insurance claim frequency data, we illustrate
the various models fitting to the empirical claim frequency distribution. Incorporation of covariates information in a
regression setting will be considered in Section 5. Results of fitting the claim frequency distribution by using various
models are given in Table 3. Based on the chi-square statistics, the Poisson distribution does not provide an adequate
fit to the motor insurance data. The score statistic (Van den Broek, 1995) of testing the null hypothesis H0: φ = 0 is
given by 592.17 (p-value 0.0001), which provides evidence that the observed zeros exceeds the zeros limit of the
Poisson distribution. In addition, the statistical significance of the proportion parameter φ in different zero-inflated
models points to the same conclusion: the Poisson distribution is inappropriate in modeling the automobile claim
frequency data.