Faculty of Economics and Business Administration Publications Database

Fitting a parametric distribution for large claims in case of censored or partitioned data

Volume: 12
Number: 2
Pages: 155 - 165
Month: April
ISSN-Print: 0167-6687
Link External Source: Online Version
Year: 1993
Keywords: Large claim distributions; Parameter estimation; Quantiles; Censored data

Hill's estimator and related quantities are commonly used to fit tails and estimate parameters of heavy-tailed claim distributions. Given a sample of size n, the estimators are based on the exact values of the largest observations; consequently, these statistics are not applicable if the largest observations are censored or available merely in partitioned form. (In practice, an important kind of censorship is caused by RBNS claims). An estimator based on empirical quantiles is proposed for a parametric family of claim distributions containing parametric Pareto, Weibull and extreme value distributions as special cases. Complete convergence and asymptotic normality are verified, and the probability of the event ‘The distance between estimator and estimand is greater than ϵ’ is shown to be of order O(exp( - dn)) for some d > 0.