The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications

Abstract

In actuarial statistics, distributions with heavy tails are of great interest to actuaries, as they represent a better description of risk exposure through a type of indicator with a certain probability. These risk indicators are used to determine companies’ exposure to a particular risk. In this paper, we present a distribution with heavy right tail, studying its properties and the behaviour of the tail. We estimate the parameters using the maximum likelihood method and evaluate the performance of these estimators using Monte Carlo. We analyse one set of simulated data and another set of real data, showing that the distribution studied can be used to model income data.