Modeling Insurance Claims with Extreme Observations: Transformed Kernel Density and Generalized Lambda Distribution

In modeling insurance claims, when there are extreme observations in the data, the commonly used loss distributions often are able to fit the bulk of the data well but fail to do so at the tail. One approach to overcome this problem is to focus on the extreme observations only and model them with the generalized Pareto distribution, as supported by extreme value theory. However, this approach discards useful information about the small and medium-sized claims, which is important for many actuarial purposes. In this article we consider modeling large skewed data using a highly flexible distribution, the generalized lambda distribution, and the recently proposed semiparametric transformed kernel density estimation. Our results suggest that both these approaches are credible options for the investigator when modeling insurance claims data that typically contain large extreme observations. In addition, even at the extreme tails they perform well when compared with the generalized Pareto distribution.