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Sea and wind: multivariate extremes at work. (English) Zbl 0921.62144

This article is devoted to the multivariate extreme value theory which is used to estimate the probability of failure of a sea-wall near the town of Petten in North Holland, Netherlands. The failure region has been obtained by coastal engineers and depends on the structure of the dike and the adjoining part of the sea bottom. This is an account of theoretical and applied work done by the Dutch participants of the European Union project “Neptune”, 1995-1997, grant MAS (marine science) 2-CT94-0081. The project as a whole aimed at creating a model for transferring extreme conditions in weather patterns to sea state conditions offshore and then to sea state conditions near shore which could threaten coastal areas. The sample consists of 828 observations of still water levels and wave heights collected during the storm events over a 13-year period. The paper sketches the probabilistic and statistical theory behind the estimation procedures used.

MSC:

62P99 Applications of statistics
86A05 Hydrology, hydrography, oceanography
62H12 Estimation in multivariate analysis
62N99 Survival analysis and censored data
60G70 Extreme value theory; extremal stochastic processes
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