On Compatibility/Incompatibility of Two Discrete Probability Distributions in the Presence of Incomplete Specification

Conditional specification of distributions is a developing area with several applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we revisit a rank–based criterion for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros under the finite discrete set up. Based on this, we primarily focus on the compatibility of two conditionals (under the finite discrete set-up) in which incomplete specification on either or both the conditional matrices are present. Compatibility in the general case are also briefly discussed. The proposed methods are finally illustrated with several examples.