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.


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


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