High quantile estimation for heavy-tailed distributions

Different estimators of high quantiles, such as x p c proposed in [N.M. Markovitch, U.R. Krieger, The estimation of heavy-tailed probability density functions, their mixtures and quantiles. Computer Networks 40 (3) (2002) 459–474], Weissman’s estimator x p w and the POT-method are considered. Regarding the estimators x p c and x p w the asymptotic normality of the logarithms of ratios of these estimators to the true value of the quantile is proved. These estimators are applied to real data of Web sessions and pages. Furthermore, bootstrap confidence intervals of x p c and x p w are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.