Modelling extreme health insurance claims using generalized Pareto distribution

Abstract

Extreme value theory has been used to develop models for describing the distribution of rare events. The generalized Pareto distribution is a very popular two parameter model for extreme events. It was first introduced by Pikands (1975). It is a family of continuous prob- ability distributions used to model extreme value above a given threshold. In this study, we determined the extreme health insurance claims from RSSB and its behavior (distribution). In the methodology the project shows how to choose a threshold. After choosing appro- priate threshold, maximum likelihood estimation method was used to estimate parameters because of its efficiency. In application, we used the diagnostic plots to show that the gener- alized Pareto distribution fit well extreme claims. Estimation of return level gives estimate of the amount of claims RSSB would pay in a given period of time. In data set, the average time elapsing between two successive realizations of the highest value itself is between 10 and 12 years with a probability between 1 10 and 1 12 . By comparing GPD and Exponential distribution, the result showed that the Exponential distribution fit data better than GPD.