Priority statement and some properties of t-lgHill estimator

Milan Stehlik (1) , Jozef Kiseľák (2) , Marijus Vaičiulis (3) , Pavlina Kalcheva Jordanova (4) , Ludy Nunez Soza (5) , Zdeněk Fabián (6) , Philipp Hermann (7) , Luboš Střelec (8) , Andres Rivera (9) , Stéphane Girard (10, 11) , Sebastián Torres (12)

1 Department of Applied Statistics [Linz]
2 Institute of Mathematics [Kosice, Slovakia]
3 Vilnius University [Vilnius]
4 Shumen University Konstantin Preslavski
5 Universidad de Tarapaca
6 CAS - Czech Academy of Sciences [Prague]
7 JKU - University of Linz - Johannes Kepler Universität Linz
8 MENDELU - Mendel University in Brno
9 USACH - Universidad de Santiago de Chile [Santiago]
10 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
11 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension
12 Departamento de Matematica [Valparaiso]

We acknowledge the priority on the introduction of the formula of t-lgHill estimator for the positive extreme value index. We provide a novelmotivation 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.

Domaines: Statistiques [math.ST]

Milan Stehlik, Jozef Kiseľák, Marijus Vaičiulis, Pavlina Kalcheva Jordanova, Ludy Nunez Soza, et al.. Priority statement and some properties of t-lgHill estimator. Extremes, 2020, 23 (3), pp.393--399. ⟨10.1007/s10687-020-00375-2⟩. ⟨hal-02540248⟩