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.
Key wordGeneralized Pareto distribution Feasible estimates Method of moments Method of probability weighted moments
This work is supported by the Ministry of Education and Science of the Republic of Serbia, Grant nos. 174012 and TR34007.
The author would like to thank the editors and the referees for their useful comments and suggestions.
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