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Asymptotic properties of mth spacings based on records

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  • Bayramoglu, Ismihan
  • Stepanov, Alexei

Abstract

In this work, the mth spacings based on record values obtained from continuous distributions are discussed. We first present distributional results for such spacings, and then, by making use of classification of distribution tails, derive asymptotic results for the mth record spacings. We also obtain strong limit results for them and illustrate our theoretical results by examples. Finally, we support our findings by data obtained from simulation experiments.

Suggested Citation

  • Bayramoglu, Ismihan & Stepanov, Alexei, 2024. "Asymptotic properties of mth spacings based on records," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s016771522400021x
    DOI: 10.1016/j.spl.2024.110052
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    References listed on IDEAS

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    1. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    2. Ahmadi, Jafar, 2020. "Characterization results for symmetric continuous distributions based on the properties of k-records and spacings," Statistics & Probability Letters, Elsevier, vol. 162(C).
    3. Dembinska, A. & Stepanov, A., 2006. "Limit theorems for the ratio of weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1454-1464, August.
    4. Balakrishnan, N. & Stepanov, A., 2008. "Asymptotic properties of the ratio of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 301-310, February.
    5. Stepanov, Alexei & Dembińska, Anna, 2022. "Limit theorems for the uppermost mth spacing based on weak geometric records," Statistics & Probability Letters, Elsevier, vol. 183(C).
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