de Haan, Laurens; Sinha, Ashoke Kumar Estimating the probability of a rare event. (English) Zbl 1105.62344 Ann. Stat. 27, No. 2, 732-759 (1999). 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. 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