Second-order refined peaks-over-treshold modelling for heavy-tailed distributions

J. Beirlant, E. Joossens, J.J.J. Segers

Research output: Contribution to journalArticleScientificpeer-review

40 Citations (Scopus)


Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit well and in such a case applies only to a small upper fraction of the data. The extension of the (G)PD proposed in this paper is able to describe the excess distribution for lower thresholds in case of heavy-tailed distributions. This yields a statistical model that can be fitted to a larger portion of the data. Moreover, estimates of tail parameters display stability for a larger range of thresholds. Our findings are supported by asymptotic results, simulations and a case study.
Original languageEnglish
Pages (from-to)2800-2815
JournalJournal of Statistical Planning and Inference
Publication statusPublished - 2009


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