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Negative dependence in the balls and bins experiment with applications to order statistics

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  • Hu, Taizhong
  • Xie, Chaode

Abstract

Dependence properties of occupancy numbers in the balls and bins experiment are studied. Applying such properties, we investigate further dependence structures of order statistics X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n of n independent random variables X1,X2,...,Xn with possibly different distributions. For 1[less-than-or-equals, slant]i s} or {Xi:n[less-than-or-equals, slant]s} then is decreasing in i for fixed s. It is also shown that in this situation, if each random variable Xk has a continuous distribution function and if Ai,s is either {Xi-1:n

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  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1342-1354
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    References listed on IDEAS

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    1. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    2. 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.
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    4. 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.
    5. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    6. 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.
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    Cited by:

    1. S. Ashrafi & M. Asadi, 2015. "On the stochastic and dependence properties of the three-state systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 261-281, April.
    2. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    3. Montes, Ignacio & Montes, Susana, 2016. "Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fr e ´ chet–Hoeffding upper bound," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 275-298.
    4. Mao, Tiantian & Hu, Taizhong, 2010. "Stochastic properties of INID progressive Type-II censored order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1493-1500, July.

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