Asymptotic Conditional Distribution of Exceedance Counts

Abstract

We investigate the asymptotic distribution of the number of exceedances amongdidentically 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 thefragility index, which represents the expected number of exceedances, given that there is at least one exceedance. Computed from the firstdRVs 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 asdincreases.