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1 results

  • Asymptotic Conditional Distribution of Exceedance Counts

  • Part of
  • Michael Falk, Diana Tichy
  • Journal:
    Advances in Applied Probability / Volume 44 / Issue 1 / March 2012
    Published online by Cambridge University Press:
    04 January 2016, pp. 270-291
    Print publication:
    March 2012
    • Article
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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.