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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
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 6 (July)
    Pages: 1342-1354

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1342-1354

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    Related research

    Keywords: Negative regression dependent Negative left tail dependent Negative right tail dependent Order statistics Generalized multinomial distribution Usual stochastic order;

    References

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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.
    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. 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.
    4. 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.
    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.
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    Cited by:
    1. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    2. 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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