Copyright © 2005 Elsevier B.V. All rights reserved.
High quantile estimation for heavy-tailed distributions
Available online 8 August 2005.
Abstract
Different estimators of high quantiles, such as 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
and the POT-method are considered. Regarding the estimators
and
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
and
are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.
Keywords: Heavy-tailed distribution; High quantile; Extreme value index; Bootstrap; Web-traffic data






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