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On the fluctuations of independent copies of moving maxima

Author

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  • Nayak, S. S.
  • Zalki, Madhusudhan

Abstract

Let {Xn, n[greater-or-equal, slanted]1} be a sequence of independent random variables (r.v.'s) with a common distribution function (d.f.) F. Define the moving maxima Yk(n)=max(Xn-k(n)+1,Xn-k(n)+2,...,Xn), where {k(n), n[greater-or-equal, slanted]1} is a sequence of positive integers. Let Yk(n)1 and Yk(n)2 be two independent copies of Yk(n). Under certain conditions on F and k(n), the set of almost sure limit points of the vector consisting of properly normalised Yk(n)1 and Yk(n)2 is obtained.

Suggested Citation

  • Nayak, S. S. & Zalki, Madhusudhan, 2000. "On the fluctuations of independent copies of moving maxima," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 351-356, December.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:4:p:351-356
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    References listed on IDEAS

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    1. Rothmann, Mark. D. & Russo, Ralph P., 1991. "Strong limiting bounds for a sequence of moving maxima," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 403-410, May.
    2. Hebbar, H. V. & Vadiraja, N., 1997. "Limit points of sequences of moving maxima," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 13-18, May.
    3. Gut, Allan, 1990. "Limit points of sample maxima," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 331-336, April.
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    1. Hebbar, H. V. & Vadiraja, N., 1997. "Limit points of sequences of moving maxima," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 13-18, May.
    2. Rothmann, Mark D., 1997. "Stability of maxima over randomly deleted sets," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 145-152, December.

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