Contingency Uniformity Measure: An approach for spread characterization in Contingency tables

  • Ratnesh Kumar Singh
  • Naveen Kumar
  • Vivek Vijay Indian Institute of Technology Jodhpur
DOI: https://doi.org/10.19139/soic-2310-5070-2878
Keywords: Entropy, Contingency Table, Maximum Entropy Principle, Probability distribution

Abstract

This paper introduces the Contingency Uniformity Measure (CUM), a normalized entropy that scales Shannon entropy to the range [0, 1], enabling fair comparisons across contingency tables of different dimensions. CUM retains key properties such as nonegativity, reaches its maximum at the uniform distribution, and satisfies weighted additivity. We formulate and solve three optimization problems, using CUM, under realistic constraints, fixed marginal distributions, a cost matrix, and cost variance. This is demonstrated through a real dataset of cost matrix obtained using distance matrix. Our results show that CUM is an effective, standardized measure for analyzing uncertainty and supporting decision-making in diverse, constraint-driven systems.
Published
2025-12-12
How to Cite
Singh, R. K., Naveen Kumar, & Vijay, V. (2025). Contingency Uniformity Measure: An approach for spread characterization in Contingency tables. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2878
Issue
Online First
Section
Research Articles
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