Improving on Estimation for the Generalized Pareto Distribution

Abstract

The generalized Pareto distribution (GPD) was widely used to model exceedances over thresholds, such as flood levels of rivers. Zhang and Stephens (2009) proposed a new estimation method for parameters of the GPD, which, based on the likelihood method and empirical Bayesian method, is free from the theoretical and computational problems suffered by traditional estimation approaches. In terms of estimation efficiency and bias, the new method outperforms other existing methods in common situations, but it may perform poorly for very heavy-tailed distributions. The new method is modified in this article to significantly improve its adaptivity. This article has supplementary material online.

Keywords:  :

• Bias
• Empirical Bayesian method
• Estimation efficiency
• Maximum likelihood estimation
• Profile likelihood function