This paper discusses the use of the peaks over threshold method for estimating long return period design values of environmental loads. Attention is focused on the results concerning the type of asymptotic extreme value distribution for use in the extrapolation to required design values obtained by such methods, which in many cases seem to indicate that the Weibull distribution for maxima is the appropriate one. It will be shown by a closer scrutiny of the underlying estimation process that very often such a conclusion cannot in fact be substantiated.
Issue Section:
Research Papers
1.
Castillo, E., 1988, “Extreme Value Theory,” Engineering, Academic Press Inc., San Diego, CA.
2.
Davison
A. C.
Smith
R. L.
1990
, “Models of Exceedances Over High Thresholds
,” Journal of the Royal Statistical Society
, Ser. B, Vol. 52
, pp. 339
–442
.3.
de Haan
L.
1990
, “Fighting the Archenemy with Mathematics
,” Statistica Neerlandica
, Vol. 44
, pp. 45
–68
.4.
de Haan, L., 1994, “Extreme Value Statistics,” Extreme Value Theory and Applications, Vol. 1, J. Galambos, J. Lechner and E. Simiu, eds., Kluwer Academic Publishers, Dordrecht and Bosten.
5.
Fisher
R. A.
Tippet
L. H. C.
1928
, “Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample
,” Proceedings, Cambridge Philosophical Society
, Vol. 24
, pp. 180
–190
.6.
Gross, J. L., Heckert, N. A., Lechner, J. A., and Simiu, E., 1994, “Novel Extreme Value Procedures: Application to Extreme Wind Data,” Extreme Value Theory and Applications, Vol. 1, J. Galambos, J. Lechner and E. Simiu, eds., Kluwer Academic Publishers, Dordrecht and Boston.
7.
Gross, J. L., Heckert, N. A., Lechner, J. A., and Simiu, E., 1995, “A Study of Optimal Extreme Wind Estimation Procedures,” Proceedings, Ninth International Conference on Wind Engineering, New Delhi, India.
8.
Hosking
J. R. M.
Wallis
J. R.
1987
, “Parameter and Quantile Estimation for the Generalized Pareto Distribution
,” Technometrics
, Vol. 29
, pp. 339
–349
.9.
Leadbetter, R. M., Lindgren, G., and Rootzen, H., 1983, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York.
10.
Naess, A., Storli, H., and Storm, L. E., 1996, “Statistical Prediction of Long Return Period Design Values,” Proceedings, 15th International Conference on Offshore Mechanics and Arctic Engineering, Florence, Italy, June, ASME, Vol. 2, pp. 17–22.
11.
Naess
A.
1998
, “Estimation of Long Return Period Design Values for Wind Speeds
,” Journal of Engineering Mechanics
, ASCE, Vol. 124
, No. 3
, pp. 252
–259
.12.
Pickands
J.
1975
, “Statistical Interference Using Order Statistics
,” Annals of Statistics
, Vol. 3
, pp. 119
–131
.13.
Simiu
E.
Filliben
J. J.
Bie´try
J.
1978
, “Sampling Errors in the Estimation of Extreme Wind Speeds
,” Journal of the Structural Division
, ASCE, Vol. 104
, pp. 491
–501
.14.
Simiu
E.
Heckert
N. A.
1996
, “Extreme Wind Distribution Tails: A ‘Peaks Over Threshold’ Approach
,” Journal of Structural Engineering
, ASCE, Vol. 122
, No. 5
, pp. 539
–547
.15.
Smith, R. L., 1989, “Extreme Value Theory,” Handbook of Applicable Mathematics, Supplement, eds., W. Ledermann, E. Lloyd, S. Vajda, and C. Alexander, John Wiley and Sons, New York, NY, pp. 437–472.
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