A New Selecting k Method of Hill’s Estimator

Jutamas Boonradsamee, Winai Bodhisuwan, Uraiwan Jaroengeratikun

Abstract

Estimating the tail index parameter is one of the primal objectives in extreme value theory (EVT). The tail index was referred directly from extreme value index (EVI) or shape parameter (ξ) of a heavy-tailed distribution. Hill’s estimator is the rst estimator which appeared and modified in the literature for the extreme value index since 1975 endless to nowadays such as smooHill estimator, Hill’s estimator in altscale, smooHill estimator in altscale [1], weighted Hill’s estimator [2]. For heavy-tailed distributions, the Hill’s estimator is still the most popular way to estimate the tail index parameter (α). Its estimate is a measure of the heaviness of the underlying distribution of tail and also asymptotically as efficient based onthe optimal index k of order statistics. Therefore, selecting the optimal a value of indexk will lead to an effective estimate of the Hill’s estimator. In this research investigated the graphical methods of Hill’s estimator, a very common way to determine a good choice for the index k is given by the so-called Hill plot. We purpose the method of quantile estimator for choice index k, to estimate the tail index of the series, which characterizes the tail behavior, especially the speed of the tail decay. The information in this study drawn from a Pareto distribution.