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

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.