期刊
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
卷 139, 期 8, 页码 2800-2815出版社
ELSEVIER
DOI: 10.1016/j.jspi.2009.01.006
关键词
Bias reduction; Hill estimator; Extended Pareto distribution; Extreme value index; Heavy tails; Regular variation; Tail empirical process; Tail probability; Weissman probability estimator
资金
- Belgian government [P6/03]
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. (C) 2009 Elsevier B.V. All rights reserved.
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