POT METHODS: A NEW INSIGHT INTO THE ESTIMATION OF EXTREME VALUE DISTRIBUTIONS – APPLICATION TO EXTREME WAVE HEIGHTS

Franck Mazas, Luc Hamm, Philippe Garat

Abstract


Within the framework of the GPD-Poisson model for determining extreme values of environmental variables, we examine the sensitivity of this methodology to the lowest and to the largest data of the sample. We show the need for a clear distinction between the threshold selecting the data to be fitted with a location parameter setting the origin of the distribution and that the introduction of this latter parameter yields stable results, consistent with the physics. We also show that the likelihood maximum of the classical model is reached at an open upper bound of the parameter space with non-null derivatives: hence, the asymptotic properties of MLE are not proven and one should be quite cautious when using it. Applications are presented with real and simulated data.

Keywords


Extremes; wave heights; POT; GPD; MLE; threshold; location parameter

References


Lehmann, E.L. (1983). Theory of point estimation. Wiley & Sons, Australia.http://dx.doi.org/10.1007/978-1-4757-2769-2

Hosking, J. R. M. (1990). L-moments: Analysis and Estimation of Distributions using Linear Combinations of Order Statistics. J. R. Statist. Soc., 52(1), 105-124.

Mazas, F., Hamm, L. (2011). A multi-distribution approach to POT methods for determining extreme wave heights. Coastal Engineering, 58, 385-394.http://dx.doi.org/10.1016/j.coastaleng.2010.12.003

Cook, R. D. (1986). Assessment of Local Influence. J. R. Statist. Soc., series B, 48(2), 133-169


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.