On the issue of convergence of certain divergence measures related to finding most nearly compatible probability distribution under the discrete set-up

In the context of finding most nearly compatible probability distributions under the discrete set-up, the role(s) of divergence measures as pseudo-distance (equivalently as measures of dissimilarity) measures are of paramount importance. For a detailed discussion on various measures of statistical divergence and its properties, see Pardo (2018) and the references cited therein. Recently, Ghosh and Balakrishnan (2015) have utilized several of such divergence measures, such as the Power divergence, and several other measures. However, in search for the most nearly compatible (or incompatible) distributions, the convergence of the iterative algorithms remains a challenging issue. In this article, we put forward a sketch of the proof regarding the convergence of the iterative algorithm(s) for certain divergence measures under some mild conditions. The proof for the more general case still remains an open problem.& COPY; 2023 Elsevier B.V. All rights reserved.