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On dispersive ordering between order statistics in one-sample and two-sample problems

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  • Khaledi, Baha-Eldin
  • Kochar, Subhash

Abstract

Let Xi:n denote the ith-order statistic of a random sample of size n from a continuous distribution with distribution function F. It is shown that if F is a decreasing failure rate (DFR) distribution, then Xi:n is less dispersed than Xj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j. Let Yj:m denote the jth-order statistic of a random sample of size m from a continuous distribution G. We prove that if F is less dispersed than G and either F or G is DFR, then Xi:n is less dispersed than Yj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j.

Suggested Citation

  • Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "On dispersive ordering between order statistics in one-sample and two-sample problems," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 257-261, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:257-261
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    References listed on IDEAS

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    1. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
    2. Bartoszewicz, J., 1987. "A note on dispersive ordering defined by hazard functions," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 13-16, September.
    3. Kochar, Subhash C., 1996. "Dispersive ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 27(3), pages 271-274, April.
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    Cited by:

    1. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    2. Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
    3. Alimohammadi, Mahdi & Esna-Ashari, Maryam & Cramer, Erhard, 2021. "On dispersive and star orderings of random variables and order statistics," Statistics & Probability Letters, Elsevier, vol. 170(C).
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    8. Van Delft, Christian & Kerbache, Laoucine & El Khoury, Hiba, 2011. "Optimal strategy for stochastic product rollover under risk using CVAR analysis," HEC Research Papers Series 958, HEC Paris.
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