  Conditional specification of distributions is a developing area with
increasing 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 setup. 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 illustrated with several examples.
