A THRESHOLD APPROACH FOR PEAKS-OVER-THRESHOLD MODELING USING MAXIMUM PRODUCT OF SPACINGS

Abstract: We propose a threshold model extending the generalized Pareto distribu-tion for exceedances over a threshold. The threshold is solely determined within the model and is shown to be super-consistent under the maximum product of spacings estimation method. We apply the model to some insurance data and demonstrate the merit of having a full parametric model for the entire data set. Key words and phrases: Exceedances, generalized Pareto distribution, maximum product of spacings, super-consistency, threshold model