Feller-Pareto and Related Distributions: Numerical Implementation and Actuarial Applications

Abstract

Actuaries model insurance claim amounts using heavy tailed probability distributions. They routinely need to evaluate quantities related to these distributions such as quantiles in the far right tail, moments or limited moments. Furthermore, actuaries often resort to simulation to solve otherwise untractable risk evaluation problems. The paper discusses our implementation of support functions for the Feller-Pareto distribution for the R package actuar. The Feller-Pareto defines a large family of heavy tailed distributions encompassing the transformed beta family and many variants of the Pareto distribution.