{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T04:59:38Z","timestamp":1778734778950,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T00:00:00Z","timestamp":1643068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003329","name":"Ministry of Economy, Industry and Competitiveness","doi-asserted-by":"publisher","award":["MTM2017-86875-C3-2-R"],"award-info":[{"award-number":["MTM2017-86875-C3-2-R"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014181","name":"Junta de Extremadura","doi-asserted-by":"publisher","award":["GR18108"],"award-info":[{"award-number":["GR18108"]}],"id":[{"id":"10.13039\/501100014181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking 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\u2013Hastings algorithm with data over the threshold and the new methods when the 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, L\u00e9vy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis\u2013Hastings algorithm.<\/jats:p>","DOI":"10.3390\/e24020178","type":"journal-article","created":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T20:38:58Z","timestamp":1643143138000},"page":"178","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4028-9668","authenticated-orcid":false,"given":"Jacinto","family":"Mart\u00edn","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Extremadura, 06006 Badajoz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8380-1898","authenticated-orcid":false,"given":"Mar\u00eda Isabel","family":"Parra","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Extremadura, 06006 Badajoz, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4604-2439","authenticated-orcid":false,"given":"Mario Mart\u00ednez","family":"Pizarro","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Centro Universitario de M\u00e9rida, Universidad de Extremadura, 06800 M\u00e9rida, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1549-7964","authenticated-orcid":false,"given":"Eva L\u00f3pez","family":"Sanju\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Centro Universitario de M\u00e9rida, Universidad de Extremadura, 06800 M\u00e9rida, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nogaj, M., Yiou, P., Parey, S., Malek, F., and Naveau, P. 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