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Priority statement and some properties of t-lgHill estimator

Abstract

We acknowledge the priority on the introduction of the formula of t-lgHill estimator for the positive extreme value index. We provide a novel motivation for this estimator based on ecologically driven dynamical systems. Another motivation is given directly by applying the general t-Hill procedure to log-gamma distribution. We illustrate the good quality of t-lgHill estimator in comparison to classical Hill estimator on the novel data of the concentration of arsenic in drinking water in the rural area of the Arica and Parinacota Region, Chile.

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Acknowledgements

Open access funding provided by Johannes Kepler University Linz. We acknowledge the very professional support of Editor-in-Chief Professor Thomas Mikosch, the unknown Associate Editor and Referee for their constructive comments.

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Correspondence to Milan Stehlík.

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We acknowledge support of research grants LIT-2016-1-SEE-023, the bilateral project Bulgaria -Austria, 2016–2019, ‘Feasible statistical modeling for extremes in ecology and finance’, BNSF, Contract number 01/8, 23/08/2017 and WTZ Project No. BG 09/2017, https:// pavlinakj.wordpress.com/. The authors are grateful also to bilateral project HU 11/2016, Proyecto UTA MAYOR 4746-19, the Slovak Research and Development Agency under the contract No. APVV-17-0568, the Czech Science Foundation under the project No. GA16-07089S and FONDECYT N1171832.

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Stehlík, M., Kiseľák, J., Vaičiulis, M. et al. Priority statement and some properties of t-lgHill estimator. Extremes 23, 493–499 (2020). https://doi.org/10.1007/s10687-020-00375-2

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  • DOI: https://doi.org/10.1007/s10687-020-00375-2

Keywords

  • T-lgHill estimator
  • Hill estimator
  • T-score estimation
  • Asymptotic normality
  • Levels of arsenic in drinking water

AMS 2000 Subject Classifications

  • 62F10
  • 62F12