Calibration of the Pareto and related distributions -a reference-intrinsic approach

TL;DR

This paper compares Bayesian and frequentist methods for calibrating Pareto distributions, highlighting the superior performance of the Reference Intrinsic approach in simulations and its practical relevance for banking capital regulation.

Contribution

It introduces and evaluates a reference-intrinsic Bayesian approach for Pareto calibration, demonstrating its advantages over traditional methods in accuracy and invariance.

Findings

Reference Intrinsic method outperforms others in simulation

All methods provide comparable estimates in real case study

Invariance under data transformation improves calibration accuracy

Abstract

We study two Bayesian (Reference Intrinsic and Jeffreys prior) and two frequentist (MLE and PWM) approaches to calibrating 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 generalised Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements