In this paper, we discuss a method to define prior distributions for the thresh-
old 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.

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