A Bayesian approach to extended models for exceedance

Abstract

In extreme value theory, the generalized Pareto distribution (GPD) is a family of continuous distribution used to model the tail of the distribution to values higher than a threshold $u$. Several works have used this method to approximate the tail of distribution. In this paper, we propose two extensions of GPD, including an additional shape parameter, to provide a more flexible distribution for exceedance. Some properties of these approximations are presented. Inference for these extensions were performed under the Bayesian paradigm, and the results showed fit improvement when compared with the standard GPD in applications to environmental and financial data.