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

Magdalena Chrapek; Jadwiga Dudkiewicz; Wiesław Dziubdziela

Applicationes Mathematicae (1997)

- Volume: 24, Issue: 2, page 189-193
- ISSN: 1233-7234

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topChrapek, Magdalena, Dudkiewicz, Jadwiga, and Dziubdziela, Wiesław. "On the limit distributions of kth order statistics for semi-pareto processes." Applicationes Mathematicae 24.2 (1997): 189-193. <http://eudml.org/doc/219161>.

@article{Chrapek1997,

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.},

author = {Chrapek, Magdalena, Dudkiewicz, Jadwiga, Dziubdziela, Wiesław},

journal = {Applicationes Mathematicae},

keywords = {extreme values; semi-Pareto process; autoregressive process; auto-regressive process; compound Poisson distribution},

language = {eng},

number = {2},

pages = {189-193},

title = {On the limit distributions of kth order statistics for semi-pareto processes},

url = {http://eudml.org/doc/219161},

volume = {24},

year = {1997},

}

TY - JOUR

AU - Chrapek, Magdalena

AU - Dudkiewicz, Jadwiga

AU - Dziubdziela, Wiesław

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

JO - Applicationes Mathematicae

PY - 1997

VL - 24

IS - 2

SP - 189

EP - 193

AB - 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.

LA - eng

KW - extreme values; semi-Pareto process; autoregressive process; auto-regressive process; compound Poisson distribution

UR - http://eudml.org/doc/219161

ER -

## References

top- [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. Zbl0686.60029
- [2] J. Gani, On the probability generating function of the sum of Markov Bernoulli random variables, J. Appl. Probab. 19A (1982), 321-326. Zbl0488.60074
- [3] M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983. Zbl0518.60021
- [4] J. Pawłowski, Poisson theorem for non-homogeneous Markov chains, J. Appl. Probab. 26 (1989), 637-642. Zbl0685.60028
- [5] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465. Zbl0727.60039
- [6] Y. H. Wang, On the limit of the Markov binomial distribution, ibid. 18 (1981), 937-942. Zbl0475.60050
- [7] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301. Zbl0658.62101

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