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

Abstract

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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.

How to cite

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Chrapek, 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

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  1. [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. [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. [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. [4] J. Pawłowski, Poisson theorem for non-homogeneous Markov chains, J. Appl. Probab. 26 (1989), 637-642. Zbl0685.60028
  5. [5] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465. Zbl0727.60039
  6. [6] Y. H. Wang, On the limit of the Markov binomial distribution, ibid. 18 (1981), 937-942. Zbl0475.60050
  7. [7] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301. Zbl0658.62101

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