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Exponentiated generalized Pareto distribution: Properties and applications towards extreme value theory

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  • Seyoon Lee
  • Joseph H. T. Kim

Abstract

The GPD is a central distribution in modelling heavy tails in many applications. Applying the GPD to actual datasets however is not trivial. In this paper we propose the Exponentiated GPD (exGPD), created via log-transform of the GPD variable, which has less sample variability. Various distributional quantities of the exGPD are derived analytically. As an application we also propose a new plot based on the exGPD as an alternative to the Hill plot to identify the tail index of heavy tailed datasets, and carry out simulation studies to compare the two.

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  • Seyoon Lee & Joseph H. T. Kim, 2019. "Exponentiated generalized Pareto distribution: Properties and applications towards extreme value theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 2014-2038, April.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:8:p:2014-2038
    DOI: 10.1080/03610926.2018.1441418
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    Cited by:

    1. Katleho Makatjane, 2022. "Forecasting Uncertainty Intervals for Return Period of Extreme Daily Electricity Consumption," International Journal of Energy Economics and Policy, Econjournals, vol. 12(4), pages 217-225, July.
    2. Se Yoon Lee & Bani K. Mallick, 2022. "Bayesian Hierarchical Modeling: Application Towards Production Results in the Eagle Ford Shale of South Texas," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 1-43, May.
    3. Oorschot, Jochem & Segers, Johan & Zhou, Chen, 2022. "Tail inference using extreme U-statistics," LIDAM Discussion Papers ISBA 2022014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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