Estimation of the Pareto and related distributions–A reference-intrinsic approach

Abstract

We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalized Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements.