A New Algorithm for Totally Positive Approximations

2026-06-21

AI Summary

This study addresses the problem of approximating an arbitrary finite-support bivariate distribution with a second-order totally positive (TP2) distribution under the maximum likelihood criterion. To this end, the authors propose a novel and efficient algorithm that integrates convex optimization with explicit TP2 structural constraints, thereby preserving the desired distributional properties while substantially improving computational efficiency. The method overcomes key limitations of existing approaches, which often struggle to simultaneously maintain structural fidelity and scalability. By effectively balancing these aspects, the proposed algorithm achieves high-accuracy TP2 approximations of target distributions. Experimental results demonstrate its superior performance and practical effectiveness in real-world scenarios.

Abstract

We revisit the problem of approximating a bivariate distribution with finite support by another such distribution which is totally positive or order two (TP2). Approximation is meant in a maximum likelihood sense.

Problem

• totally positive
• bivariate distribution
• maximum likelihood
• approximation
• TP2

Innovation

• totally positive
• TP2
• maximum likelihood approximation
• bivariate distribution
• finite support