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

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Boonmee, Therdsak; Tasena, Santi: Measure of complete dependence of random vectors (2016)
  2. Bairamov, Ismihan; Khaledi, Baha-Eldin; Shaked, Moshe: Stochastic comparisons of order statistics and their concomitants (2014)
  3. Irincheeva, Irina; Cantoni, Eva; Genton, Marc G.: A non-Gaussian spatial generalized linear latent variable model (2012)
  4. Fernández-Ponce, J.M.; Pellerey, F.; Rodríguez-Griñolo, M.R.: A characterization of the multivariate excess wealth ordering (2011)
  5. Belzunce, Félix; Ruiz, José M.; Suárez-Llorens, Alfonso: On multivariate dispersion orderings based on the standard construction (2008)
  6. Embrechts, Paul; Puccetti, Giovanni: Bounds for functions of multivariate risks (2006)
  7. Kolev, Nikolai; Dos Anjos, Ulisses; Mendes, Beatriz Vaz de M.: Copulas: a review and recent developments (2006)
  8. Sancetta, Alessio; Satchell, Stephen: The Bernstein copula and its applications to modeling and approximations of multivariate distributions (2004)
  9. Hu, Taizhong; Khaledi, Baha-Eldin; Shaked, Moshe: Multivariate hazard rate orders (2003)
  10. Bedford, Tim; Cooke, Roger M.: Vines -- a new graphical model for dependent random variables. (2002)
  11. Müller, Alfred; Scarsini, Marco: Stochastic comparison of random vectors with a common copula. (2001)
  12. Kaiser, Mark S.; Cressie, Noel: The construction of multivariate distributions from Markov random fields (2000)
  13. Xu, Susan H.; Li, Haijun: Majorization of weighted trees: A new tool to study correlated stochastic systems (2000)
  14. Li, Haijun; Scarsini, Marco; Shaked, Moshe: Dynamic linkages for multivariate distributions with given nonoverlapping multivariate marginals (1999)
  15. Scarsini, Marco; Shaked, Moshe: Distributions with known initial hazard rate functions (1999)
  16. Shaked, Moshe; Shanthikumar, J.George: Two variability orders (1998)
  17. Li, Haijun; Scarsini, Marco; Shaked, Moshe: Linkages: A tool for the construction of multivariate distributions with given nonoverlapping multivariate marginals (1996)