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

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  • 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

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    1. Mohammad Ahsanullah & Fazil Aliev, 2011. "A characterization of geometric distribution based on weak records," Statistical Papers, Springer, vol. 52(3), pages 651-655, August.
    2. 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.
    3. Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    4. Vervaat, Wim, 1973. "Limit theorems for records from discrete distributions," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 317-334, October.
    5. Dembinska, A. & Stepanov, A., 2006. "Limit theorems for the ratio of weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1454-1464, August.
    6. Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
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