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Priority statement and some properties of t-lgHill estimator

Extremes volume 23, pages 493–499 (2020)Cite this article

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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Authors and Affiliations

  1. Department of Applied Statistics, Linz Institute of Technology, Johannes Kepler University in Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Milan Stehlík

  2. Institute of Statistics, Universidad de Valparaíso, Valparaíso, Chile

    Milan Stehlík

  3. Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, USA

    Milan Stehlík

  4. Institute of Mathematics, Faculty of Science, P. J. Šafárik University in Košice, Košice, Slovakia

    Jozef Kiseľák

  5. Vilnius University Institute of Data Science and Digital Technologies, Akademijos 4, LT-08663, Vilnius, Lithuania

    Marijus Vaičiulis

  6. Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, Universitetska Str. 115, 9700, Shumen, Bulgaria

    Pavlina Jordanova

  7. Departamento de Matemática, Facultad de Ciencias, Universidad de Tarapacá, Avenida 18 de Septiembre 2222, Casilla 7-D, Arica, Chile

    Ludy Núñez Soza

  8. Institute of Computer Science of the Czech Academy of Sciences, Pod vodárenskou věží 2, 18200, Prague, Czech Republic

    Zdeněk Fabián

  9. Department of Applied Statistics, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Philipp Hermann

  10. Department of Statistics and Operation Analysis (FBE), Mendel University in Brno, Zemědelská 1, 61300, Brno, Czech Republic

    Luboš Střelec

  11. Departamento de Geografia, Universidad de Chile, Avda. Portugal 84, Santiago, Chile

    Andrés Rivera

  12. Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000, Grenoble, France

    Stéphane Girard

  13. Department of Mathematics, Federico Santa María Technical University, Valparaíso, Chile

    Sebastián Torres

  14. Instituto de Convervación Biodiversidad y territorio, Facultad de Ciencias Forestales y Recursos NAturales, Universidad Austral de Chile, Valdivia, 5090000, Chile

    Andrés Rivera

Authors
  1. Milan Stehlík
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  2. Jozef Kiseľák
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  3. Marijus Vaičiulis
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  4. Pavlina Jordanova
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  5. Ludy Núñez Soza
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  6. Zdeněk Fabián
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  7. Philipp Hermann
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  8. Luboš Střelec
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  9. Andrés Rivera
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  10. Stéphane Girard
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  11. Sebastián Torres
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Corresponding author

Correspondence to Milan Stehlík.

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The authors declare that they have no conflict of interest.

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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