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Dependence structures of multivariate Bernoulli random vectors

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  • Hu, Taizhong
  • Xie, Chaode
  • Ruan, Lingyan
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    Abstract

    In some situations, it is difficult and tedious to check notions of dependence properties and dependence orders for multivariate distributions supported on a finite lattice. The purpose of this paper is to utilize a newly developed tool, majorization with respect to weighted trees, to lay out some general results that can be used to identify some dependence properties and dependence orders for multivariate Bernoulli random vectors. Such a study gives us some new insight into the relations between the concepts of dependence.

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    Bibliographic Info

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

    Volume (Year): 94 (2005)
    Issue (Month): 1 (May)
    Pages: 172-195

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    Handle: RePEc:eee:jmvana:v:94:y:2005:i:1:p:172-195

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    Related research

    Keywords: Weakly positive (negatively) associated Positively (negatively) supermodular dependent Strongly positive (negative) orthant dependent Positive (negative) orthant dependent Supermodular order Concordance order Majorization with respect to weighted trees Probability trees;

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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, Elsevier, vol. 88(1), pages 138-151, January.
    2. Block, Henry W. & Fang, Zhaoben, 1990. "Setwise independence for some dependence structures," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 32(1), pages 103-119, January.
    3. Frostig, Esther, 2003. "Ordering ruin probabilities for dependent claim streams," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 93-114, February.
    4. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 73(1), pages 107-119, April.
    5. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 35(1), pages 12-30, October.
    6. Frostig, Esther, 2001. "Comparison of portfolios which depend on multivariate Bernoulli random variables with fixed marginals," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 319-332, December.
    7. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 61(1), pages 86-101, April.
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    Cited by:
    1. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.

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