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

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.