Advances in Applied Probability

Asymptotic conditional distribution of exceedance counts

Michael Falk and Diana Tichy

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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

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

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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