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Further developments on sufficient conditions for negative dependence of random variables

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  • Hu, Taizhong
  • Yang, Jianping

Abstract

Let W=(W1,...,Wn) be a random vector of n independent random variables, and let R=(R1,...,Rn) be another random vector having the permutation distribution on {1,2,...,n}, independent of W. If the Wi's are ordered in the likelihood ratio order [resp. the hazard rate order, the reversed hazard rate order, and the usual stochastic order], it is shown that (WR1,WR2,...,WRn) is negatively regression dependent [resp. negatively right tail dependent, negatively left tail dependent, and negatively associated]. Several applications of the main results are also given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:369-381
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    References listed on IDEAS

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    1. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    2. Hu, Taizhong & Hu, Jinjin, 1999. "Sufficient conditions for negative association of random variables," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 167-173, November.
    3. 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.
    4. 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.
    5. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "Stochastic Comparisons and Dependence among Concomitants of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 262-281, May.
    6. Frostig, Esther, 2001. "A comparison between homogeneous and heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 59-71, August.
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    Cited by:

    1. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    2. Li, Yanhai & Ou, Jinwen, 2022. "Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion," European Journal of Operational Research, Elsevier, vol. 297(3), pages 904-916.
    3. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.

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