Sea and Wind: Multivariate Extremes at Work

Multivariate extreme value theory is used to estimate the probability of failure of a sea-wall near the town of Petten in Noord Holland, The Netherlands. The sample consists of 828 observations of still water levels and wave heights collected during storm events over a 13-year period. The paper sketches the probabilistic and statistical theory behind the estimation procedures used.

[1]  Sidney I. Resnick,et al.  Estimating the limit distribution of multivariate extremes , 1993 .

[2]  N. Booij,et al.  Wave conditions along the Dutch coast , 1993 .

[3]  L. Haan Estimating exceedance probabilities in higher-dimensional space , 1994 .

[4]  A. Ledford,et al.  Statistics for near independence in multivariate extreme values , 1996 .

[5]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[6]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[7]  L. Haan,et al.  A moment estimator for the index of an extreme-value distribution , 1989 .

[8]  Laurens de Haan,et al.  Slow Variation and Characterization of Domains of Attraction , 1984 .

[9]  S. T. Pwa,et al.  De basispeilen langs de Nederlandse kust: Fysisch onderzoek , 1993 .

[10]  Jonathan A. Tawn,et al.  Statistics of Multivariate Extremes , 1990 .

[11]  L. de Haan,et al.  Estimating the spectral measure of an extreme value distribution , 1997 .

[12]  S. Coles,et al.  Modelling Extreme Multivariate Events , 1991 .

[13]  G. Dargahi‐Noubary On estimation of failure probability , 1988 .

[14]  Jonathan A. Tawn,et al.  Statistical Methods for Multivariate Extremes: An Application to Structural Design , 1994 .

[15]  S. Resnick Extreme Values, Regular Variation, and Point Processes , 1987 .

[16]  Masaaki Sibuya,et al.  Bivariate extreme statistics, I , 1960 .

[17]  C. Valk Selection of storm events and estimation of exceedance frequencies of significant wave height for five North Sea locations , 1994 .

[18]  Richard L. Smith,et al.  Multivariate Threshold Methods , 1994 .

[19]  L. de Haan,et al.  On the estimation of the exceedance probability of a high level , 1990 .