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Estimating exceedance probabilities in higher-dimensional space. (English) Zbl 0807.60051

Summary: An asymptotic theory is developed for the estimation of the exceedance probability of a two-dimensional vector \((w,z)\) whose components are very large numbers. In fact we assume \(w\) and \(z\) so large that if \(n\) is the number of available observations and \(F\) the underlying distribution function, the mean number of exceedances above the level \((w,z)\), namely \(n\{1 - F(w,z)\}\) is very small. Our results enable us e.g. to estimate the probability of a flood at either one of two places along a river. Asymptotic normality of the estimated exceedance probability is proved so that an asymptotic confidence interval can be constructed. Conditions are in the area of extreme value theory.

MSC:

60G70 Extreme value theory; extremal stochastic processes
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