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

TL;DR

This paper proposes a transformation-based method to estimate the shape parameter of a generalized Pareto distribution, improving bias and mean squared error over existing estimators.

Contribution

It introduces a transformation approach that leverages explicit Pareto estimators to enhance the estimation of the generalized Pareto shape parameter.

Findings

Transformation improves estimator performance

Probability weighted estimator shows reduced bias

Method achieves lower MSE

Abstract

Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using transformed observations, based on the probability weighted method is tested. It was found to improve the performance of the probability weighted estimator and performs good with respect to bias and MSE.