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

• Autorzy: Magdalena Chrapek , Jadwiga Dudkiewicz , Wiesław Dziubdziela
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

extreme values   semi-Pareto process   autoregressive process  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 2
• Strony: 189-193

Daty

wydano

1997

otrzymano

1995-10-30

poprawiono

1996-01-18

Twórcy

autor

Magdalena Chrapek

• Institute of Mathematics, Pedagogical University, ul. M. Konopnickiej 21, 25-406 Kielce, Poland

autor

Jadwiga Dudkiewicz

• Department of Mathematics, Kielce University of Technology, al. Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland

autor

Wiesław Dziubdziela

• Faculty of Civil and Environment Engineering, Department of Building Constructions, Częstochowa Technical University, ul. Akademicka 3, 42-200 Częstochowa, Poland

Bibliografia

• [1] B. C. Arnold and J. T. Hallett, A characterization of the Pareto process among stationary stochastic processes of the form $X_n$= c min($X_n-1$,$Y_n$), Statist. Probab. Lett. 8 (1989), 377-380.
• [2] J. Gani, On the probability generating function of the sum of Markov Bernoulli random variables, J. Appl. Probab. 19A (1982), 321-326.
• [3] M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
• [4] J. Pawłowski, Poisson theorem for non-homogeneous Markov chains, J. Appl. Probab. 26 (1989), 637-642.
• [5] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465.
• [6] Y. H. Wang, On the limit of the Markov binomial distribution, ibid. 18 (1981), 937-942.
• [7] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301.