Estimation for the Generalized Pareto Distribution Using Maximum Likelihood and Goodness of Fit

Abstract

In this article, we introduce a new estimator for the generalized Pareto distribution, which is based on the maximum likelihood estimation and the goodness of fit. The asymptotic normality of the new estimator is shown and a small simulation. From the simulation, the performance of the new estimator is roughly comparable with maximum likelihood for positive values of the shape parameter and often much better than maximum likelihood for negative values.

Keywords:

• Asymptotic distribution
• Estimation
• Generalized pareto distribution
• Maximum likelihood

Mathematics Subject Classification:

• Primary 60G70
• Secondary 60F05, 62F10, 62F12

Acknowledgments

The first author was supported by a grant of the Swiss National Science Foundation. The second author was supported by NNSFC Grant 10801038.