On the limit distributions of kth order statistics for semi-pareto processes

Magdalena Chrapek; Jadwiga Dudkiewicz; Wiesław Dziubdziela

ArticleOriginal scientific text

Title

On the limit distributions of kth order statistics for semi-pareto processes

Authors ¹, ², ³

Affiliations

Institute of Mathematics, Pedagogical University, ul. M. Konopnickiej 21, 25-406 Kielce, Poland
Department of Mathematics, Kielce University of Technology, al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland
Faculty of Civil and Environment Engineering, Department of Building Constructions, Częstochowa Technical University, ul. Akademicka 3, 42-200 Częstochowa, Poland

Abstract

Asymptotic properties of the kth largest values for semi-Pareto processes are investigated. Conditions for convergence in distribution of the kth largest values are given. The obtained limit laws are represented in terms of a compound Poisson distribution.

Keywords

ENG

extreme values, semi-Pareto process, autoregressive process

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Title

On the limit distributions of kth order statistics for semi-pareto processes

Affiliations

Abstract

Keywords

Bibliography