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Probability inequalities via negative dependence for random variables conditioned on order statistics

Author

Listed:
  • Henry W. Block
  • Vanderlei Bueno
  • Thomas H. Savits
  • Moshe Shaked

Abstract

Distributions are studied which arise by considering independent and identically distributed random variables conditioned on events involving order statistics. It is shown that these distributions are negatively dependent in a very strong sense. Furthermore, bounds are found on the distribution functions. The conditioning events considered occur naturally in reliability theory as the time to system failure for k‐out‐of‐n systems. An application to systems formed with “second‐hand” components is given.

Suggested Citation

  • Henry W. Block & Vanderlei Bueno & Thomas H. Savits & Moshe Shaked, 1987. "Probability inequalities via negative dependence for random variables conditioned on order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 547-554, August.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:4:p:547-554
    DOI: 10.1002/1520-6750(198708)34:43.0.CO;2-B
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
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    Cited by:

    1. Hu, Taizhong & Yang, Jianping, 2004. "Further developments on sufficient conditions for negative dependence of random variables," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 369-381, February.
    2. Hu, Taizhong & Xie, Chaode, 2006. "Negative dependence in the balls and bins experiment with applications to order statistics," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1342-1354, July.
    3. Hu, Taizhong & Hu, Jinjin, 1999. "Sufficient conditions for negative association of random variables," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 167-173, November.

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