Estimating the parameters of the three-parameter Generalized Pareto Distribution using the Method of Moments and Pickands' Method

Abstract

When studying and evaluating the probabilities of rare events, the Generalized Pareto Distribution (GPD) is used, which includes the exponential, Pareto, and Beta distributions as special cases. Therefore, the focus is on the Generalized Pareto Distribution. The researcher applied the GPD according to the sample size in several applications, including the analysis of survival times of stomach cancer patients. It was found that the data follow a three-parameter Generalized Pareto Distribution based on the Kolmogorov-Smirnov (K-S) test, the Anderson-Darling (A-D) test, and the Chi-square goodness-of-fit test.

After applying the Mean Squared Error (MSE) criterion to both the Method of Moments and Pickands’ method, the researcher concluded that Pickands’ method is the best estimation method for the three parameters (α, k, μ), while the Method of Moments is the second-best estimation approach for these parameters.