Which model can be used to model auto claims following a Poisson distribution?

The model that is best suited for modeling auto claims following a Poisson distribution is the zero-inflated model. This model is specifically designed to handle data that has an excess of zeros, which is common in count data like auto claims—where many individuals may have no claims at all.

A zero-inflated model works by combining two processes: one that generates only zeros and another that follows a Poisson distribution for the positive counts. In the context of auto claims, many drivers do not file claims over a specific period, resulting in a significant number of zero claims. The zero-inflated model captures this phenomenon effectively while also modeling the actual counts of claims from those who do make a claim.

While the hurdle model is another approach that could be considered, it operates differently. The hurdle model assumes that there are two separate processes: one to determine whether the count is zero or above zero and another to model the counts when they are above that hurdle. This model would typically be used when there is a clear separation between the zero counts and the counts above zero.

The heterogeneity model, although useful in some contexts for accounting for differences in risk among individuals, does not inherently accommodate the modifications needed for excess zeros in count data like the zero-in