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

Year: 2025

Type: article

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.

Source: Statistics Optimization & Information Computing

DOI: 10.19139/soic-2310-5070-2878

Authors: Ratnesh Kumar Singh, Naveen Kumar, Vivek Vijay

Institution: Indian Institute of Technology Jodhpur

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: University Grants Commission

OpenAlex ID: W7115089172

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