Which distribution and link function is most appropriate for modeling the impact of miles driven on personal auto insurance claims?

The Poisson distribution combined with a log link function is appropriate for modeling the impact of miles driven on personal auto insurance claims because this situation typically involves count data. In insurance claims, the number of claims filed over a given period can be thought of as discrete events that occur independently. The Poisson distribution is particularly tailored for modeling such count data where the mean rate of occurrence is constant.

By using a log link function, the model allows the predicted number of claims to increase exponentially with the miles driven. This is sensible because as a driver accumulates more miles, it is reasonable to expect that the likelihood of filing a claim would increase in a non-linear fashion. The log link function ensures that predicted values remain positive, which is critical for count data where negative numbers don’t make sense.

Other distributions and link functions either do not suit the nature of the data or do not align well with the impact of continuous predictors like miles driven. For instance, the normal distribution is not ideal for count data since it allows for negative values and assumes a different error structure. The binomial distribution is suited for binary outcomes and wouldn’t apply well to counting the number of claims. The gamma distribution is typically used for modeling continuous, positively skewed data but is not appropriate