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In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the. adj. 1. Of, relating to, located at, or constituting a margin, a border, or an edge: the marginal strip of beach;. Next (Theorem 7), the existence of probability distributions with given marginals is studied under typically weaker assumptions, than those which are required. Bivariate distributions with minimum and maximum correlations for given marginal distributions are characterized. Such extremal distributions were first. The last decade has seen a remarkable development of the "Marginal and Moment Problems" as a research area in Probability and Statistics. Distributions With Given Marginals and Statistical Modelling. Editors: Cuadras, Carles M., Fortiana, Josep, Rodríguez-Lallena, José A. (Eds.) Free Preview. Thus, for instance, we immediately obtain that the tractability of MAP inference in trees or tree-like graphs yields an efficient algorithm for marginal. Bivariate distributions with minimum and maximum correlations for given marginal distributions are characterized. Such extremal distributions. distributions with given marginals is studied under typically weaker assump- tions, than those which are required by the use of Theorem 1. Nevertheless, classical random variables appear implicitly in an SQMF if some marginals of the SQMF satisfy some conditions; variables of.