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Title: Baseline methods for estimating the parameters of Generalized Pareto distributions Authors:  M Isabel Parra Arevalo - Universidad de Extremadura (Spain)
Mario M Pizarro - Universidad de Extremadura (Spain)
Jacinto Martin Jimenez - Universidad de Extremadura (Spain)
Eva Lopez Sanjuan - Universidad de Extremadura (Spain) [presenting]
Abstract: In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto distribution (GPD), only the observations above a certain threshold are considered. To make the most of the information provided by the observations, and improve the accuracy in Bayesian parameter estimation, we present two new Bayesian methods to estimate the parameters of the GPD. They take into account the whole data set from the baseline distribution, and the existing relations between the baseline and the limit GPD parameters, in order to define highly informative priors. We make a comparison between the Bayesian Metropolis-Hastings algorithm with data over the threshold and the new methods when baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Levy and Cauchy distributions. Nevertheless, the methods would be applicable to many other baseline distributions, through finding relations between baseline and GPD parameters via studies of simulations.