High quantile estimation for heavy-tailed distributions

N. M. Markovich

doi:10.1016/j.peva.2005.07.014

High quantile estimation for heavy-tailed distributions

N. M. Markovich

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Different estimators of high quantiles, such as xpc 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 xpw and the POT-method are considered. Regarding the estimators xpc and xpw 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 xpc and xpw are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.

Original language	English
Pages (from-to)	178-192
Number of pages	15
Journal	Performance Evaluation
Volume	62
Issue number	1-4
DOIs	https://doi.org/10.1016/j.peva.2005.07.014
State	Published - 1 Oct 2005
Externally published	Yes

Keywords

Bootstrap
Extreme value index
Heavy-tailed distribution
High quantile
Web-traffic data

ASJC Scopus subject areas

Software
Modeling and Simulation
Hardware and Architecture
Computer Networks and Communications

Access to Document

10.1016/j.peva.2005.07.014

Cite this

@article{c1868969aad94623a5bb73e631d87f17,

title = "High quantile estimation for heavy-tailed distributions",

abstract = "Different estimators of high quantiles, such as xpc 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 xpw and the POT-method are considered. Regarding the estimators xpc and xpw 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 xpc and xpw are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.",

keywords = "Bootstrap, Extreme value index, Heavy-tailed distribution, High quantile, Web-traffic data",

author = "Markovich, \{N. M.\}",

year = "2005",

month = oct,

day = "1",

doi = "10.1016/j.peva.2005.07.014",

language = "English",

volume = "62",

pages = "178--192",

journal = "Performance Evaluation",

issn = "0166-5316",

publisher = "Elsevier B.V.",

number = "1-4",

}

TY - JOUR

T1 - High quantile estimation for heavy-tailed distributions

AU - Markovich, N. M.

PY - 2005/10/1

Y1 - 2005/10/1

N2 - Different estimators of high quantiles, such as xpc 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 xpw and the POT-method are considered. Regarding the estimators xpc and xpw 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 xpc and xpw are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.

AB - Different estimators of high quantiles, such as xpc 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 xpw and the POT-method are considered. Regarding the estimators xpc and xpw 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 xpc and xpw are constructed for modelled data of different heavy-tailed distributions as well as for Web-traffic data.

KW - Bootstrap

KW - Extreme value index

KW - Heavy-tailed distribution

KW - High quantile

KW - Web-traffic data

UR - https://www.scopus.com/pages/publications/24144449029

U2 - 10.1016/j.peva.2005.07.014

DO - 10.1016/j.peva.2005.07.014

M3 - Article

AN - SCOPUS:24144449029

SN - 0166-5316

VL - 62

SP - 178

EP - 192

JO - Performance Evaluation

JF - Performance Evaluation

IS - 1-4

ER -

High quantile estimation for heavy-tailed distributions

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this