An alternative approach for compatibility of two discrete conditional distributions

TL;DR

This paper introduces a new rank-based method for assessing the compatibility of two discrete conditional distributions, especially useful when zeros are involved, enhancing the analysis of conditional specifications.

Contribution

It proposes an alternative, rank-based approach for determining compatibility of two discrete conditional distributions, including cases with zeros, which is a novel contribution.

Findings

The method effectively identifies compatible distributions.

It simplifies compatibility analysis with zeros in the distributions.

Illustrated with multiple practical examples.

Abstract

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.