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Abstract Consider two families of candidate conditional densities (or probability mass functions), f (x | y) ;y ∈ S y and f (y | x): x ∈ S x. This article investigates necessary and sufficient conditions for the existence of a joint density (or joint probability mass function) f (x, y) with the given families as its associated conditional densities. This supplements previous work that has addressed the question of uniqueness of f (x, y) assuming its existence.
Arnold et al. (Wed,) studied this question.
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