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Limiting behavior of the ratio of kth records

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  • Jasiński, Krzysztof

Abstract

Let R0(k),R1(k),… be kth record values derived from samples consisting of independent identically distributed discrete random variables. In the present paper, using the theory of regular variation, we discuss the asymptotic behavior of Rn+m(k)∕Rn(k) as n→∞.

Suggested Citation

  • Jasiński, Krzysztof, 2019. "Limiting behavior of the ratio of kth records," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 29-34.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:29-34
    DOI: 10.1016/j.spl.2019.02.004
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    References listed on IDEAS

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    1. Bairamov, Ismihan & Stepanov, Alexei, 2006. "A note on large deviations for weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1449-1453, August.
    2. Dembinska, A. & Stepanov, A., 2006. "Limit theorems for the ratio of weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1454-1464, August.
    3. Balakrishnan, N. & Stepanov, A., 2008. "Asymptotic properties of the ratio of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 301-310, February.
    4. Enkelejd Hashorva & Alexei Stepanov, 2012. "Limit theorems for the spacings of weak records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 163-180, February.
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