Probability distributions with given multivariate marginals and given dependence structure. (English) Zbl 0773.62034

Summary: This paper provides a method of constructing multivariate distributions where both univariate marginals and a correlation matrix are given. An extension to multivariate marginals and a given intercorrelation matrix is also obtained. This method yields a family of distributions which are totally linear regressive and may be useful to generate exact samples for testing statistical models, to study structural models where the covariance structure is given, and to justify a statistical distance with mixed variables.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
62J05 Linear regression; mixed models
62H25 Factor analysis and principal components; correspondence analysis
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