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Dynamic Linkages for Multivariate Distributions with Given Nonoverlapping Multivariate Marginals

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  • Li, Haijun
  • Scarsini, Marco
  • Shaked, Moshe

Abstract

One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. Liet al.(1996) introduced an analogous tool, called linkage, which is useful for handling multivariate distributions with givenmultivariatemarginals. The goal of the present paper is to introduce a new kind of linkage, called thedynamic linkage, which can usefully handle multivariate life distributions (that is, distributions of non-negative random variables) by taking advantage of the time dynamics of the underlying lifetimes. Like the linkages of Liet al.(1996), the new dynamic linkage can be used for the study of multivariate distributions with given multivariate marginals by emphasizing the separate roles of the dependence structureamongthe given multivariate marginals and the dependence structurewithineach of the nonoverlapping marginals. Preservation of some setwise positive dependence properties, from the dynamic linkage functionLto the joint distributionFand vice versa, are studied. When two different distribution functions are associated with the same dynamic linkage (that is, have the same setwise dependence structure) we show that the cumulative hazard order among the corresponding multivariate marginal distributions implies an overall stochastic dominance between the two underlying distribution functions.

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  • Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1999. "Dynamic Linkages for Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 54-77, January.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:54-77
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    References listed on IDEAS

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    1. Shaked, Moshe & Shanthikumar, J. George, 1991. "Dynamic multivariate aging notions in reliability theory," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 85-97, June.
    2. Moshe Shaked & J. George Shanthikumar, 1990. "Multivariate Stochastic Orderings and Positive Dependence in Reliability Theory," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 545-552, August.
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    5. Li, Haijun & Scarsini, Marco & Shaked, Moshe, 1996. "Linkages: A Tool for the Construction of Multivariate Distributions with Given Nonoverlapping Multivariate Marginals," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 20-41, January.
    6. Marco Scarsini, 1988. "Multivariate stochastic dominance with fixed dependence structure," Post-Print hal-00542234, HAL.
    7. Block, Henry W. & Fang, Zhaoben, 1990. "Setwise independence for some dependence structures," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 103-119, January.
    8. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
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    Cited by:

    1. Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2012. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers 12003, Concordia University, Department of Economics.
    2. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    3. Nabil Kazi-Tani & Didier Rullière, 2017. "On a construction of multivariate distributions given some multidimensional marginals," Working Papers hal-01575169, HAL.

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