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.
