What is the most appropriate distribution for modeling the aggregate auto claims for a specific block of business?

The most appropriate distribution for modeling aggregate auto claims for a specific block of business is the GLM with a Tweedie response. This is because the Tweedie distribution is particularly suited for handling data that consists of a mixture of small and large claims, which is a common scenario in insurance claims.

In the context of insurance, aggregate claims data often includes a significant number of small-value claims and a smaller number of very large claims, leading to a data structure that can be characterized by a Tweedie distribution, specifically a compound Poisson-gamma distribution. The Tweedie family of distributions allows for three important aspects: it can model both the occurrence of claims (as in a Poisson process) and the distribution of claim sizes, especially when there are many zeros (no claims) and a continuous range of positive values.

In contrast, while other distributions such as the normal, Poisson, and exponential distributions have their applications, they do not suitably capture the characteristics of aggregate auto claims. The normal distribution assumes a symmetric distribution with no bounds, which is not realistic for claims data that is often skewed and has a lower bound of zero. The Poisson distribution models count data, which might be useful for counting the number of claims but does