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Asymptotic properties of the ratio of order statistics

Author

Listed:
  • Balakrishnan, N.
  • Stepanov, A.

Abstract

Let X1,n[less-than-or-equals, slant]X2,n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn,n be the order statistics obtained from a sample from a continuous distribution and Zi,j,n=Xj,n/Xi,n be the ratio of order statistics. In this paper, asymptotic properties of Zi,j,n are discussed. Specifically, we make use of the theory of regular variation to derive weak and strong limit results for Zi,j,n.

Suggested Citation

  • Balakrishnan, N. & Stepanov, A., 2008. "Asymptotic properties of the ratio of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 301-310, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:3:p:301-310
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    References listed on IDEAS

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    1. Dembinska, A. & Stepanov, A., 2006. "Limit theorems for the ratio of weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1454-1464, August.
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    Cited by:

    1. Jasiński, Krzysztof, 2019. "Limiting behavior of the ratio of kth records," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 29-34.
    2. Bayramoglu, Ismihan & Stepanov, Alexei, 2024. "Asymptotic properties of mth spacings based on records," Statistics & Probability Letters, Elsevier, vol. 208(C).

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