Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations
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Cristiano Villa [1]
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[1] University of Kent
University of Kent
City of Canterbury, Reino Unido
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 1, 2017, págs. 95-118
- Idioma: inglés
- DOI: 10.1007/s11749-016-0501-7
- Texto completo no disponible (Saber más ...)
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Resumen
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.
