Advances in Applied Probability

Asymptotic conditional distribution of exceedance counts

Michael Falk and Diana Tichy

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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.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 1 (2012), 270-291.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1331216653

Digital Object Identifier
doi:10.1239/aap/1331216653

Mathematical Reviews number (MathSciNet)
MR2951555

Zentralblatt MATH identifier
1236.62005

Subjects
Primary: 62G32: Statistics of extreme values; tail inference
Secondary: 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory

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

Citation

Falk, Michael; Tichy, Diana. Asymptotic conditional distribution of exceedance counts. Adv. in Appl. Probab. 44 (2012), no. 1, 270--291. doi:10.1239/aap/1331216653. https://projecteuclid.org/euclid.aap/1331216653


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