Fitting the generalized Pareto distribution to data based on transformations of order statistics

ABSTRACT

Generalized Pareto distribution (GPD) has been widely used to model exceedances over thresholds. In this article we propose a new method called weighted nonlinear least squares (WNLS) to estimate the parameters of the GPD. The WNLS estimators always exist and are simple to compute. Some asymptotic results of the proposed method are provided. The simulation results indicate that the proposed method performs well compared to existing methods in terms of mean squared error and bias. Its advantages are further illustrated through the analysis of two real data sets.

KEYWORDS:

• Generalized Pareto distribution
• transformations
• order statistics
• least squares
• parameter estimation

2000 MSC:

• 62F10
• 62G30

Acknowledgments

The authors thank reviewers, an associate editor and the editor for their helpful corrections, comments and suggestions which led to an improved version of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Additionally, this project was partially supported by the Natural Science Foundation of China [No. 11701021], National Bureau of Statistics of China [No. 2016LZ42], National Bureau of Statistics of China [No. 2017LZ35], Beijing Postdoctoral Science Foundation [No. 2016ZZ-30], Science and Technology Program of Beijing Education Commission [No. KM201610005020].