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ABSTRACT
The generalized Pareto distribution (GPD) is widely used for extreme values over a threshold. Most existing methods for parameter estimation either perform unsatisfactorily when the shape parameter k is larger than 0.5, or they suffer from heavy computation as the sample size increases. In view of the fact that k > 0.5 is occasionally seen in numerous applications, including two illustrative examples used in this study, we remedy the deficiencies of existing methods by proposing two new estimators for the GPD parameters. The new estimators are inspired by the minimum distance estimation and the M-estimation in the linear regression. Through comprehensive simulation, the estimators are shown to perform well for all values of k under small and moderate sample sizes. They are comparable to the existing methods for k < 0.5 while perform much better for k > 0.5.
Supplementary Materials
Technical details: The PDF file provides additional simulation results based on the Type II censored data: the proposed methods are compared with the EPM when the censoring rate is set as 10%, 30%, and 40% (PDF file).
Source code: The R file contains the R code to implement the proposed M-estimation and weighted M-estimation (R file).
Acknowledgments
The authors thank the editor, associate editor, and two anonymous referees for their constructive comments and suggestions that have considerably improved the article. This work is supported by Natural Science Foundation of China (71601138) and Singapore AcRF Tier 1 funding (#R-266-000-081-133 and #R-266-000-095-112).