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Bounds based on greatest convex minorants for moments of record values

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  • Raqab, Mohammad Z.

Abstract

Let Yk,n denote the nth k-record value (upper) of an infinite sequence of independent, identically distributed random variables with common continuous distribution function F. We derive bounds for the expected values of Yk,n based on greatest convex minorants (Moriguti's method). We also present numerical comparisons between bounds obtained by Cauchy-Schwarz inequality and Moriguti's method.

Suggested Citation

  • Raqab, Mohammad Z., 1997. "Bounds based on greatest convex minorants for moments of record values," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 35-41, November.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:1:p:35-41
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    References listed on IDEAS

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    1. Stam, A. J., 1985. "Independent poisson processes generated by record values and inter-record times," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 315-325, April.
    2. Balakrishnan, N., 1993. "A simple application of binomial--negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 301-305, November.
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    Cited by:

    1. Raqab, Mohammad Z., 2010. "Evaluations of the mean residual lifetime of an m-out-of-n system," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 333-342, March.
    2. Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    3. Tomasz Rychlik, 2001. "Stability of Order Statistics under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 877-894, December.
    4. Mariusz Bieniek, 2015. "Optimal evaluations for the bias of trimmed means of $$k$$ k th record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 437-460, May.
    5. Gajek, L. & Okolewski, A., 2001. "Improved Steffensen type bounds on expectations of record statistics," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 205-212, November.
    6. Z. Raqab, Mohammad, 2003. "P-Norm bounds for moments of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 393-402, October.

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