On compatibility/incompatibility of two discrete probability distributions in the presence of incomplete specification

TL;DR

This paper introduces a rank-based criterion to assess the compatibility of two discrete probability distributions under incomplete and complete conditional specifications, including cases with zeros, with practical examples.

Contribution

It proposes a novel rank-based method for determining compatibility of conditional distributions in finite discrete settings, addressing cases with zeros and incomplete specifications.

Findings

The rank-based criterion effectively identifies compatible distributions.

The method applies to cases with zeros in the distributions.

Illustrative examples demonstrate practical utility.

Abstract

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.