We show how both Poisson regression and recurrent events models can be used to model the number of claims to expect on a car insurance policy. We also show that the same is true when these models are extended to include a random effect/frailty. We then look at the effect of different assumptions made regarding the distribution of this random effect/frailty, through simulated data sets, one where we do not know the true distribution and several where we controlled the distribution and variance of the random effect/frailty. The results showed that the choice of frailty did seem to have an impact on the estimation of expected number of claims. They also indicated that the choice of distribution to use for the frailty was more important for data with a higher degree of heterogeneity than for data with a lower degree of heterogeneity.