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Second-order refined peaks-over-threshold modelling for heavy-tailed distributions |
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| Authors: | Jan Beirlant Elisabeth Joossens Johan Segers |
| Affiliation: | 1. Department of Mathematics and Leuven Statistics Research Centre, Katholieke Universiteit Leuven, Celestijnenlaan 200b, B-3001 Heverlee, Belgium;2. Joint Research Centre, European Commission, Via Fermi 2749, 21027 Ispra (VA), Italy;3. Institut de statistique, Université catholique de Louvain, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium |
| Abstract: | 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. |
| Keywords: | Bias reduction Hill estimator Extended Pareto distribution Extreme value index Heavy tails Regular variation Tail empirical process Tail probability Weissman probability estimator |
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