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

Authors

  • Ratnesh Kumar Singh Department of Mathematics, Indian Institute of Technology Jodhpur, 342030, Rajasthan, India
  • Naveen Kumar Department of Mathematics, Indian Institute of Technology Jodhpur, 342030, Rajasthan, India
  • Vivek Vijay Department of Mathematics, Indian Institute of Technology Jodhpur, 342030, Rajasthan, India

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.

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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, 15(3), 1741–1757. https://doi.org/10.19139/soic-2310-5070-2878

Issue

Vol. 15 No. 3 (2026)

Section

Research Articles

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