Estimating exceedance probabilities in higher-dimensional space
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 10 (4) , 765-780
- https://doi.org/10.1080/15326349408807321
Abstract
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 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 theoryKeywords
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