Estimation of the shape parameter of a generalized Pareto distribution based on a transformation to Pareto distributed variables

摘要

Random variables of the generalized Pareto distribution, can be transformedto that of the Pareto distribution. Explicit expressions exist for the maximumlikelihood estimators of the parameters of the Pareto distribution. Theperformance of the estimation of the shape parameter of generalized Paretodistributed using transformed observations, based on the probability weightedmethod is tested. It was found to improve the performance of the probabilityweighted estimator and performs good with respect to bias and MSE.