A tale of two curves‎: ‎Exploring the unexpected relationship between the Lorenz curve and the ROC curve

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics and Statistics‎, ‎Faculty of Energy and Data Sciences, Behbahan Khatam Alanbia University of Technology‎, ‎Behbahan‎, ‎Iran

2 Department of Computer Science‎, ‎Faculty of Mathematical Sciences‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran

3 Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Iran

10.22034/jsmta.2026.24527.1216

Abstract

‎This paper provides a conceptual and methodological synthesis of the relationship between two tools that originate from different disciplines: the Lorenz curve, widely used to study economic inequality, and the receiver operating characteristic curve, widely used to evaluate binary classification and predictive discrimination. Building on established results linking the Gini coefficient to the area under the receiver operating characteristic curve, the study examines their relationship from a broader ranking-based and distribution-based perspective, clarifying their mathematical connections, distributional foundations, and distinct interpretations through analytical examples, Monte Carlo simulations, and applied evaluations under different sample sizes and class imbalance conditions. By clarifying these connections and examining their empirical behavior beyond idealized settings, the study provides a cross-disciplinary framework for interpreting ranking-based measures in both inequality measurement and predictive classification.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 7, Issue 1
January 2026
Pages 87-111

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History

  • Receive Date: 05 May 2026
  • Revise Date: 06 September 2026
  • Accept Date: 18 September 2026
  • First Publish Date: 18 September 2026
  • Publish Date: 01 January 2026

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