  Conditional specification of distributions is a developing area with many
applications. In the finite discrete case, a variety of compatible conditions
can be derived. In this paper, we propose an alternative approach to study the
compatibility of two conditional probability distributions under the finite
discrete set up. A technique based on rank-based criterion is shown to be
particularly convenient for identifying compatible distributions corresponding
to complete conditional specification, including the case with zeros. The
proposed methods are finally illustrated with several examples.
