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Compatible Conditional Distributions

Barry C. Arnold and S. James Press
Journal of the American Statistical Association
Vol. 84, No. 405 (Mar., 1989), pp. 152-156
DOI: 10.2307/2289858
Stable URL: http://www.jstor.org/stable/2289858
Page Count: 5
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Compatible Conditional Distributions
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Abstract

Consider two families of candidate conditional densities (or probability mass functions), {f(x ∣ y); y ∈ Sy} and {f(y ∣ x): x ∈ Sx}. 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.

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