Modelling Excesses over High Thresholds, with an Application

In many areas of application the extremes of some process may be modelled by considering only its exceedances of a high threshold level. The natural parametric family for such excesses for continuous parent random variables, the generalized Pareto distribution, is closely related to the classical extreme-value distributions. Here its basic properties are discussed, with some ideas for graphical exploration of data. Maximum likelihood estimation of parameters in the presence of covariates is considered, and techniques for checking fit based on residuals and a score test developed.

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