Abstract
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.
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Bruun, J.T. and Tawn, J.A., A comparison of joint probability models and structure variable approaches for the estimation of coastal design levels, Technical Report. Neptune project T400: A Bivariate Simulation Study, (1995).
Bruun, J.T. and Tawn, J.A., “Comparison of approaches for estimating the probability of coastal flooding,” Applied Statistics, to appear (1998).
Coles, S.G. and Tawn, J.A., “Modelling extreme multivariate events,” J. Royal Statist. Soc. series B, (1991).
Coles, S.G. and Tawn, J.A., “Statistical methods for multivariate extremes: an application to structural design,” Appl. Statist. 43, 1–48, (1994).
Dekkers, A., Einmahl, J., and Haan, L. de, “A moment estimator for the index of an extreme-value distribution,” Ann. Statist. 17, 1833–1855, (1989).
Dijk, V. and Haan, L. de, “On the estimation of the exceedence probability of a high level.” Order Statistics and Nonparametrics: Theory and Applications. (P.K. Sen and I.A. Salama, ed), Elsevier, Amsterdam, 1992.
Dillingh, D. et al., De basispeilen langs de Nederlandse kust, Technical Report DGW-93.023, Rijks Instituut voor Kust en Zee, Rijkswaterstaat, 1993.
Draisma, G., Haan, L. de, Peng, L., and Sinha, A.K., Reports Neptune T400 EUR 4, 5, 6, 7, 8, 9, 10, 12; Reports EUR/RIKZ 96.2 and 96.3, 1996, 1997. Available at http://www.cs.few.eur.nl/few/people/ldehaan.
Einmahl, J., Haan, L. de, and Piterbarg, V., “A nonparametric estimator for the spectral measure for extremes,” Technical Report, 1997.
Einmahl, J., Haan, L. de, and Sinha, A.K., Estimating the spectral measure of an extreme value distribution to appear in Stoch Proc. Appl. (1997).
Feller, W., An Introduction to Probability Theory and Its Applications, Vol. II. Wiley, New York, 1966.
Geffroy, J., Contributions à la théorie des valeurs extrèmes. Publ. Inst. Statist. Univ. Paris 7/8, 37–185. 1958, (1959).
Gumbel, E.J., “Distribution des valeurs extrèemes en plusieurs dimensions.” Publ. Inst. Statist. Univ. Paris 9, 171–173, (1960).
Haan, L. de, “Slow variation and characterization of domains of attraction,” in Statistical Extremes and Applications (J. Tiago de Oliveira, ed), Reidel, Dordrecht, 1984.
Haan, L. de, Estimating Exceedance Probabilities in Higher-Dimensional Space. Commun. Statist Stoch Models 10, 765–780, (1994).
Haan, L. de and Resnick, S.I., Estimating the limit distribution of multivariate extremes. Commun. Statist. Stoch Models 9, 275–309. A corrected version (1995) is available from the authors, 1993.
Haan, L. de and Sinha, A.K., Estimation of the Failure Probability. Technical Report, 1997.
Huang, X., “Statistics of bivariate extremes.”, Thesis, Erasmus University Rotterdam. Tinbergen Institute Research” series no. 22, 1992.
Hurdle, D., Matlab routines for offshore to onshore transformation of wave parameters at the “Pettemer zeewering”, Distributed through the Delft Hydraulics ftp site, 1995.
Hurdle, D., “Prediction of the wave conditions at Petten.” Alkyon: file DAVID.WOR, November 10, 1996.
Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate extreme values,” Biometrika, 83, 169–187, (1997).
Marle, J.G.A. van, Personal communication. December 30, 1994.
Marle, J.G.A. van, Hydraulic design conditions. Memo RIKZ /Rijkswaterstaat, June 17, 1996.
Meer, J.W. van der, Golfoploop en golfverslag bij dijken. Technical Report H638, WL Delft, in opdracht van Rijkswaterstaat, 1993.
Resnick, S.I., Extreme Values, regular variation and point processes, Springer, New York, 1987.
Roskam, B. and Hoekema, D., “Readmemx.dos: Description of recorded data on waves, wind and water level at five locations in the North sea.” Readme file accompanying RIKZ data files, May 1996.
Ronde, J.G. de et al., “Wave conditions along the Dutch coast at considerable water depth.” Ministerie van Verkeer en Waterstaat, rapport RIKZ-95.024, 1995.
Sibuya, M., “ Bivariate extreme statistics,” Ann. Inst. Stat. Math. 11, 195–210, (1960).
Sinha, A.K., “Estimating Failure Probability when failure is rare: multidimensional case.” Thesis, Erasmus University Rotterdam. Tinbergen Institute Research series no. 165, 1997.
Smith, R.L., “Extreme Value theory,” in Handbook of Applicable Mathematics (W. Ledermann, ed), vol. 7. Wiley, New York, 1990.
Smith, R.L., “Multivariate threshold methods”. in Galambos et al: Extreme value theory and applications, Kluwer, Dordrecht, 225–248, 1994.
Smith, R.L., Tawn, J.A., and Yuen, H.K., “Statistics of multivariate extremes,” Int. Statist. Rev. 58, 47–58, (1990).
Valk, C.F. de, “Selection of storm events and estimation of exceedence frequencies of significant wave height for five North sea locations,” Technical Report H1931, Delft Hydraulics, 1994.
Valk, C.F. de, “Estimation of frequencies of failure of coastal structures from offshore data of environmental loads,” Technical Report, Delft Hydraulics, February 1996.
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de Haan, L., de Ronde, J. Sea and Wind: Multivariate Extremes at Work. Extremes 1, 7–45 (1998). https://doi.org/10.1023/A:1009909800311
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DOI: https://doi.org/10.1023/A:1009909800311