Bayesian Estimation of the Threshold of a Generalised Pareto Distribution for Heavy-Tailed Observations
Abstract
In this paper, we discuss a method to define prior distributions for the threshold of a generalised Pareto distribution, in particular when its applications are directed to heavy-tailed data. We propose to assign prior probabilities to the order statistics of a given set of observations. In other words, we assume that the threshold coincides to one of the data points. We show two ways of defining a prior: by assigning equal mass to each order statistic, that is a uniform prior, and by considering the worth that every order statistic has in representing the true threshold. Both proposed priors represent a scenario of minimal information, and we study their adequacy through simulation exercises and by analysing two applications from insurance and from finance.
Keywords
Cite
@article{arxiv.1604.01268,
title = {Bayesian Estimation of the Threshold of a Generalised Pareto Distribution for Heavy-Tailed Observations},
author = {Cristiano Villa},
journal= {arXiv preprint arXiv:1604.01268},
year = {2016}
}