swMATH ID: 1332 Software Authors: Li, Haijun; Scarsini, Marco; Shaked, Moshe Description: 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. Homepage: http://www.sciencedirect.com/science/article/pii/S0047259X96900020 Keywords: standard construction; copula function; dependence structure; linkage function; given multivariate marginals; setwise positive dependence properties; joint distribution; strong stochastic dominance order; overall stochastic dominance Related Software: copula; copula; BaM; FOCI; robustbase; Cubature; GMRFLib; R; ismev Referenced in: 20 Publications
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### Referenced by 36 Authors

 6 Shaked, Moshe 4 Scarsini, Marco 3 Li, Haijun 2 Khaledi, Baha-Eldin 1 Amsler, Christine 1 Bayramoğlu, Ismihan G. 1 Bedford, Tim 1 Belzunce, Félix 1 Boonmee, Therdsak 1 Cantoni, Eva 1 Cooke, Roger Marvin 1 Cressie, Noel A. C. 1 dos Anjos, Ulisses U. 1 Embrechts, Paul 1 Fernández-Ponce, José María 1 Genton, Marc G. 1 Griessenberger, Florian 1 Hu, Taizhong 1 Irincheeva, Irina 1 Junker, Robert R. 1 Kaiser, Mark S. 1 Kazi-Tani, Nabil 1 Kolev, Nikolai 1 Mendes, Beatriz Vaz de Melo 1 Müller, Alfred 1 Pellerey, Franco 1 Puccetti, Giovanni 1 Rodríguez-Griñolo, M. R. 1 Ruiz, José-María 1 Rullière, Didier 1 Sancetta, Alessio 1 Shanthikumar, Jeyaveerasingam George 1 Suarez-Llorens, Alfonso 1 Tasena, Santi 1 Trutschnig, Wolfgang 1 Xu, Susan H.
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### Referenced in 14 Serials

 6 Journal of Multivariate Analysis 2 Mathematics of Operations Research 1 Advances in Applied Probability 1 Journal of Mathematical Analysis and Applications 1 The Annals of Statistics 1 Journal of Statistical Planning and Inference 1 Insurance Mathematics & Economics 1 Statistics & Probability Letters 1 Econometric Reviews 1 Probability in the Engineering and Informational Sciences 1 Econometric Theory 1 Stochastic Models 1 Electronic Journal of Statistics 1 Journal of Agricultural, Biological, and Environmental Statistics

### Referenced in 5 Fields

 15 Statistics (62-XX) 14 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)