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

2009/01/12 by Jan Beirlant, Beirlant, Jan, Elisabeth Joossens +3 · 1 citation
Economics, Econometrics and Finance · Environmental Science · Mathematics · #62F12 #62G30 (Secondary) #62G32 (Primary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0901.1518

openalex publication_date 2009/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Perturbation-based Inference for Extreme Value Index

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