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A simple application of binomial--negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants

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  • Balakrishnan, N.

Abstract

In this note, we present an alternate way of obtaining the sharp bound for expected values of order statistics derived by Moriguti (1953) based on the principle of greatest convex minorants. The formula presented here using an application of binomial--negative binomial relationship, in addition to being simpler to use for numerical computations, also yields explicit bounds for a few extreme order statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:18:y:1993:i:4:p:301-305
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    Citations

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    Cited by:

    1. Huang, J. S., 1997. "Sharp bounds for the expected value of order statistics," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 105-107, April.
    2. 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.
    3. Anna Dembińska, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 262-264, August.
    4. Nickos Papadatos, 1997. "Exact Bounds for the Expectations of Order Statistics from Non-Negative Populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(4), pages 727-736, December.
    5. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.

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