Comparative analysis of parametric Lorenz curves and alternative convex models with isotonic regression for estimating the Lorenz curve

Document Type : Research Paper

Author

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

Abstract

This study develops a systematic comparative framework for estimating Lorenz curves and Gini coefficients, addressing key methodological gaps in measuring income inequality. We employ the Generalized Mean Squared Error (GMSE) to compare several parametric models (such as polynomial, beta, and established functional forms) with isotonic regression as a non-parametric alternative. Extensive Monte Carlo simulations using log-normal and Pareto distributions show that isotonic regression consistently achieves higher accuracy than parametric approaches. An application to Iranian household income data (n = 18,809) further confirms these results. Based on data characteristics and research objectives, the findings offer practical guidance for selecting appropriate estimation methods.

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Main Subjects

References

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History

  • Receive Date: 02 May 2025
  • Revise Date: 30 November 2025
  • Accept Date: 05 February 2026

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