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Linkages: A tool for the construction of multivariate distributions with given nonoverlapping multivariate marginals. (English) Zbl 0863.62049

Summary: One of the most useful tools for handling multivariate distributions with given univariate marginals 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 given multivariate marginals by emphasizing the separate roles of the dependence structure between the given multivariate marginals, and the dependence structure within each of the nonoverlapping marginals.
Preservation of some setwise positive dependence properties, from the linkage function \(L\) to the joint distribution \(F\) and 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory

Software:

Linkages
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