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Discrete records: Limit theorems for their spacings and generation methods

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  • Pakhteev, A.
  • Stepanov, A.

Abstract

Let X1,X2,… be independent and identically distributed random variables with support on non-negative integers and X(n)(n≥1) denote the corresponding sequence of discrete record values. In the present paper, we derive weak and strong limit results for the spacings of discrete record values X(n+m)−X(n)(n→∞) and discuss generation algorithms of discrete records.

Suggested Citation

  • Pakhteev, A. & Stepanov, A., 2019. "Discrete records: Limit theorems for their spacings and generation methods," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 134-142.
    • Handle: RePEc:eee:stapro:v:148:y:2019:i:c:p:134-142
    DOI: 10.1016/j.spl.2019.01.016
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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. Stepanov, Alexei & Berred, Alexandre & Nevzorov, Valery B., 2016. "Concomitants of records: Limit results, generation techniques, correlation," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 184-188.
    3. Pakhteev, A. & Stepanov, A., 2016. "Simulation of Gamma records," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 204-212.
    4. Nevzorov, V.B. & Stepanov, A., 2014. "Records with confirmation," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 39-47.
    5. Vervaat, Wim, 1973. "Limit theorems for records from discrete distributions," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 317-334, October.
    6. Narayanaswamy Balakrishnan & Alexei Stepanov, 2013. "Runs Based on Records: Their Distributional Properties and an Application to Testing for Dispersive Ordering," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 583-594, September.
    7. 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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