High quantile estimation for heavy-tailed distributions

Authors:
N. M. Markovich
Affiliations:
Institute of Control Sciences Russian Academy of Sciences, Profsoyuznaya Str. 65, 117997 Moscow, Russian Federation
Venue:
Performance Evaluation - Performance 2005
Year:
2005

Citing 3
Cited 1

Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems

Journal of Multivariate Analysis
Modelling extremal events: for insurance and finance

Modelling extremal events: for insurance and finance
The estimation of heavy-tailed probability density functions, their mixtures and quantiles

Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic

A general model for long-tailed network traffic approximation

The Journal of Supercomputing

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Abstract

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.