Linkages: A tool for the construction of multivariate distributions with given nonoverlapping multivariate marginals

Marco Scarsini, Moshe Shaked () and Haijun Li
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Moshe Shaked: University of Arizona
Haijun Li: University of Washington [Seattle]

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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. The goal of the present paper is to introduce an analogous tool, called the linkage function, that can be used for the study of multivariate distributions with givenmultivariatemarginals by emphasizing the separate roles of the dependence structurebetweenthe given multivariate marginals, and the dependence structurewithineach of the nonoverlapping marginals. Preservation of some setwise positive dependence properties, from the linkage functionLto the joint distributionFand vice versa, are studied. When two different distribution functions are associated with the same linkage function (that is, have the same setwise dependence structure) we show that strong stochastic dominance order among the corresponding multivariate marginal distributions implies an overall stochastic dominance between the two underlying distribution functions.

Keywords: copula; given marginals; dependence structure; setwise positive dependence; stochastic order; standard construction (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (13)

Published in Journal of Multivariate Analysis, 1996, Vol. 56, N°1, pp. 20-41. ⟨10.1006/jmva.1996.0002⟩

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Journal Article: Linkages: A Tool for the Construction of Multivariate Distributions with Given Nonoverlapping Multivariate Marginals (1996)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00541800

DOI: 10.1006/jmva.1996.0002

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