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

• Autorzy: Jadwiga Dudkiewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

consecutive-m-out-of-n system; moving minima; compound Poisson distribution; order statistics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1998-1999
• Tom: 25
• Numer: 1
• Strony: 19-28

Daty

wydano

1998

otrzymano

1996-07-11

poprawiono

1997-01-25

Twórcy

autor

Jadwiga Dudkiewicz

• Institute of Mathematics, Technical University of Kielce, Tysiąclecia PP 7, 25-314 Kielce, Poland

Bibliografia

• [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.
• [2] E. R. Canfield and W. P. McCormick, Asymptotic reliability of consecutive k-out-of-n systems, J. Appl. Probab. 29 (1992), 142-155.
• [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.
• [4] J. Dudkiewicz, Asymptotic of extremes of moving minima in arrays of independent random variables, Demonstratio Math. 29 (1996), 715-721.
• [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.
• [6] R. J. Serfling, A general Poisson approximation theorem, Ann. Probab. 3 (1975), 726-731.
• [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).