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March 2012 Asymptotic conditional distribution of exceedance counts
Michael Falk, Diana Tichy
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Adv. in Appl. Probab. 44(1): 270-291 (March 2012). DOI: 10.1239/aap/1331216653

Abstract

We investigate the asymptotic distribution of the number of exceedances among d identically distributed but not necessarily independent random variables (RVs) above a sequence of increasing thresholds, conditional on the assumption that there is at least one exceedance. Our results enable the computation of the fragility index, which represents the expected number of exceedances, given that there is at least one exceedance. Computed from the first d RVs of a strictly stationary sequence, we show that, under appropriate conditions, the reciprocal of the fragility index converges to the extremal index corresponding to the stationary sequence as d increases.

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Michael Falk. Diana Tichy. "Asymptotic conditional distribution of exceedance counts." Adv. in Appl. Probab. 44 (1) 270 - 291, March 2012. https://doi.org/10.1239/aap/1331216653

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1236.62005
MathSciNet: MR2951555
Digital Object Identifier: 10.1239/aap/1331216653

Subjects:
Primary: 62G32
Secondary: 60G70 , 62E20

Keywords: copula , D-norm , Exceedance over high threshold , extremal index , fragility index , generalized Pareto distribution (GPD) , GPD copula , multivariate extreme value theory , peaks-over-threshold approach

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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