Abstract
In hydrologic risk analysis, the use of exceedance statistics are very important. In this sense, we construct a random threshold model based on bivariate order statistics. The exact distribution of exceedance statistics is calculated under some well-known copulas such as independent and Farlie-Gumbel-Morgenstern (FGM) copulas. Furthermore, numerical results are provided for expected value and variance of exceedance statistics under independent and Farlie-Gumbel-Morgenstern copulas. The application of the model in hydrology is also discussed.
Highlights
Exceedance statistics and random threshold models are very useful tools in real life applications
A bivariate exceedance model is constructed based on bivariate order statistics
Probability of exceedance statistics are calculated under some well-known copulas for small sample sizes
Summary
Exceedance statistics and random threshold models are very useful tools in real life applications. Exceedance probability, bivariate order statistics, bivariate distributions, random threshold model, hydrologic risk. In [7] and [9] bivariate random threshold models are composed based on concomitants of order statistics. A bivariate random threshold model based on bivariate order statistics is considered. We have a training sample which consists of bivariate random variables that represent ‡ood peak and ‡ood volume of n hydrological stations in a certain location, in the past year. We have a bivariate control sample which consists of bivariate random variables that represent ‡ood peak and ‡ood volume of m hydrological stations in the same location, in the coming year. By using the minimum ‡ood peak and minimum ‡ood volume in training sample, the random threshold model is constructed.
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