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Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations.

Lookup NU author(s): Dr Cristiano VillaORCiD

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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 with 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 finance.

Publication metadata

Author(s): Villa C

Publication type: Article

Publication status: Published

Journal: TEST

Year: 2017

Volume: 26

Pages: 95–118

Print publication date: 01/03/2017

Online publication date: 05/08/2016

Acceptance date: 14/07/2016

Date deposited: 20/05/2020

ISSN (print): 1133-0686

ISSN (electronic): 1863-8260

Publisher: Springer

URL: https://doi.org/10.1007/s11749-016-0501-7

DOI: 10.1007/s11749-016-0501-7

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