Correcting Certain Estimation Methods for the Generalized Pareto Distribution

Generalized Pareto distributions (GPD) are widely used for modeling excesses over high thresholds. When its shape parameter is positive, the GPD has a finite upper bound that is a function of the distribution parameters. A well-known problem when estimating GPD parameters is inconsistency with the sample data, which is that one or more sample observations exceed the estimated upper bound. This paper proposes a new, general technique to overcome the inconsistency problem and improve performance of the existing GPD estimation methods. The technique is successfully applied to method-of-moments and method-of-probability-weighted-moments estimates, and, due to its flexibility, can be also applied to other estimation methods and distributions.