Estimating the probability of a rare event.(English)Zbl 1105.62344

Summary: Let $$(X_{1},Y_{1}), (X_{2},Y_{2}),\dots,(X_{n},Y_{n})$$ be a random sample from a bivariate distribution function $$F$$ which is in the domain of attraction of a bivariate extreme value distribution function $$G$$. A subset $$C$$ of $$\mathbb{R}^{2}$$ is given, which contains none of the observations. We shall give an asymptotic confidence interval for $$\text{Pr}((X_{i},Y_{i}) \in C)$$ under certain conditions.

MSC:

 62G32 Statistics of extreme values; tail inference 62G15 Nonparametric tolerance and confidence regions 62N99 Survival analysis and censored data 62H99 Multivariate analysis
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