Abstract
Abstract Let P 1(k 1), P m (k m ) be given k j-variate discrete marginal distributions defined in the same probability space. The problem is to define a q-variate distribution having the distributions P j (k j ) as marginals. The task is easy to solve if q = k 1 + k 2 +⋯+ k m (i.e. all marginals are non-overlapping) and all given marginals are independent (orthogonal). In this case the common distribution is uniquely defined as the product of marginals. We consider the cases when 1. the given marginals have one or more common components and 2. the dependence structure between some components of different marginals is given. Necessary and sufficient conditions for existence of common distribution are given, an algorithm for construction is presented and several practical examples demonstrated.
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Tiit, EM. (2002). Existence of Multivariate Distributions with Given Marginals. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_24
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DOI: https://doi.org/10.1007/978-94-017-0061-0_24
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