Journal of Multivariate Analysis
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Nonparametric tail estimation using a double bootstrap method
Computational Statistics & Data Analysis
Analysis and modeling of World Wide Web traffic for capacity dimensioning of Internet access lines
Performance Evaluation - Special issue on performance and control of network systems
Performance Evaluation - Special issue on internet performance modelling
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
M|G|Infinity Input Processes: A Versatile Class of Models for Network Traffic
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
High quantile estimation for heavy-tailed distributions
Performance Evaluation - Performance 2005
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This paper is devoted to the estimation of heavy-tailed probability density functions (p.d.f.s), their mixtures and high quantiles. We discuss the relevance of this issue in teletraffic engineering and propose a new combined estimation technique for such p.d.f.s. The "tail" of the p.d.f, is estimated by a parametric tail model and its "body" by a non-parametric method in terms of a finite linear combination of trigonometric functions. To provide the minimum of the mean-squared error of the estimation, the parameters of the parametric and non-parametric parts are estimated by means of the bootstrap method and the structural risk minimization method. The latter parameters are determined by the number of extreme-valued data that are used in Hill's estimate of the tail index and the number of terms and coefficients of the linear combination. The new method is illustrated using some relevant mixtures of heavy-tailed p.d.f.s and applied to construct a high-quantile estimate. Furthermore, its effectiveness is shown by an application to real data arising from Web-traffic characteristics.