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Relations for product moments and covariances of kth records from discrete distributions


  • Krzysztof Jasiński

    () (Nicolaus Copernicus University)


Abstract The aim of this paper is to establish recurrence relations satisfied by product moments and covariances of kth records arising from discrete distributions. They will be evaluated for geometric underlying distribution. Then we use these results to obtain formulas for correlation coefficients of geometric kth records. We consider all three known types of kth records: strong, ordinary, and weak.

Suggested Citation

  • Krzysztof Jasiński, 2018. "Relations for product moments and covariances of kth records from discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 125-141, February.
  • Handle: RePEc:spr:metrik:v:81:y:2018:i:2:d:10.1007_s00184-017-0637-9
    DOI: 10.1007/s00184-017-0637-9

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    References listed on IDEAS

    1. Vervaat, Wim, 1973. "Limit theorems for records from discrete distributions," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 317-334, October.
    2. Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    3. Mohammad Raqab & Tomasz Rychlik, 2011. "Bounds for the mean residual life function of a k-out-of-n system," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 361-380, November.
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