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

Villa, Cristiano (2016) Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations. TEST, 26 (1). pp. 95-118. ISSN 1133-0686. (doi:10.1007/s11749-016-0501-7) (KAR id:57598)


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.

Item Type: Article
DOI/Identification number: 10.1007/s11749-016-0501-7
Uncontrolled keywords: Extreme values; Generalised Pareto distribution; Heavy tails; KullbackÔÇôLeibler divergence; Self-information loss
Subjects: H Social Sciences > HA Statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Cristiano Villa
Date Deposited: 30 Sep 2016 15:10 UTC
Last Modified: 16 Feb 2021 13:37 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Villa, Cristiano.

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