# Compound Poisson approximation for extremes of moving minima in arrays of independent random variables

Applicationes Mathematicae (1998)

- Volume: 25, Issue: 1, page 19-28
- ISSN: 1233-7234

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topDudkiewicz, Jadwiga. "Compound Poisson approximation for extremes of moving minima in arrays of independent random variables." Applicationes Mathematicae 25.1 (1998): 19-28. <http://eudml.org/doc/219191>.

@article{Dudkiewicz1998,

abstract = {We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.},

author = {Dudkiewicz, Jadwiga},

journal = {Applicationes Mathematicae},

keywords = {consecutive-m-out-of-n system; moving minima; compound Poisson distribution; order statistics; order statistic; consecutive--out-of- system; weak convergence},

language = {eng},

number = {1},

pages = {19-28},

title = {Compound Poisson approximation for extremes of moving minima in arrays of independent random variables},

url = {http://eudml.org/doc/219191},

volume = {25},

year = {1998},

}

TY - JOUR

AU - Dudkiewicz, Jadwiga

TI - Compound Poisson approximation for extremes of moving minima in arrays of independent random variables

JO - Applicationes Mathematicae

PY - 1998

VL - 25

IS - 1

SP - 19

EP - 28

AB - We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.

LA - eng

KW - consecutive-m-out-of-n system; moving minima; compound Poisson distribution; order statistics; order statistic; consecutive--out-of- system; weak convergence

UR - http://eudml.org/doc/219191

ER -

## References

top- [1] A. D. Barbour, L. H. Y. Chen and W. L. Loh, Compound Poisson approximation for nonnegative random variables via Stein's method, Ann. Probab. 20 (1992), 1843-1866. Zbl0765.60015
- [2] E. R. Canfield and W. P. McCormick, Asymptotic reliability of consecutive k-out-of-n systems, J. Appl. Probab. 29 (1992), 142-155. Zbl0758.60093
- [3] O. Chryssaphinou and S. G. Papastavridis, Limit distribution for a consecutive k-out-of-n: F system, Adv. Appl. Probab. 22 (1990), 491-493. Zbl0713.60093
- [4] J. Dudkiewicz, Asymptotic of extremes of moving minima in arrays of independent random variables, Demonstratio Math. 29 (1996), 715-721. Zbl0879.60054
- [5] S. G. Papastavridis, A limit theorem for the reliability of a consecutive-k-out-of-n system, Adv. Appl. Probab. 19 (1987), 746-748. Zbl0626.60086
- [6] R. J. Serfling, A general Poisson approximation theorem, Ann. Probab. 3 (1975), 726-731. Zbl0321.60018
- [7] A. M. Zubkov, Estimates for sums of finitely dependent indicators and for the time of first occurrence of a rare event, Probabilistic Problems of Discrete Mathematics, Trudy Mat. Inst. Steklov. 177 (1986), 33-46, 207 (in Russian). Zbl0605.60034

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