Title: Second-order Refined Peaks-over-threshold Modelling for Heavy-tailed Distributions
Authors: BEIRLANT JanJOOSSENS ElisabethSEGERS Johan
Citation: JOURNAL OF STATISTICAL PLANNING AND INFERENCE vol. 139 no. 8 p. 2800-2815
Publisher: ELSEVIER SCIENCE BV
Publication Year: 2009
JRC Publication N°: JRC49723
ISSN: 0378-3758
URI: http://publications.jrc.ec.europa.eu/repository/handle/JRC49723
DOI: 10.1016/j.jspi.2009.01.006
Type: Articles in Journals
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.
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