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Histogram-Based Interpolation of the Lorenz Curve and Gini Index for Grouped Data

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  • Yves Tillé
  • Matti Langel

Abstract

In grouped data, the estimation of the Lorenz curve without taking into account the within-class variability leads to an overestimation of the curve and an underestimation of the Gini index. We propose a new strictly convex estimator of the Lorenz curve derived from a linear interpolation-based approximation of the cumulative distribution function. Integrating the Lorenz curve, a correction can be derived for the Gini index that takes the intraclass variability into account.

Suggested Citation

  • Yves Tillé & Matti Langel, 2012. "Histogram-Based Interpolation of the Lorenz Curve and Gini Index for Grouped Data," The American Statistician, Taylor & Francis Journals, vol. 66(4), pages 225-231, November.
    • Handle: RePEc:taf:amstat:v:66:y:2012:i:4:p:225-231
    DOI: 10.1080/00031305.2012.734197
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    Cited by:

    1. Yves Tillé, 2016. "The legacy of Corrado Gini in survey sampling and inequality theory," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 167-176, August.
    2. Jurgita Markevičiūtė & Jolita Bernatavičienė & Rūta Levulienė & Viktor Medvedev & Povilas Treigys & Julius Venskus, 2022. "Impact of COVID-19-Related Lockdown Measures on Economic and Social Outcomes in Lithuania," Mathematics, MDPI, vol. 10(15), pages 1-20, August.
    3. Biewen, Martin & Fitzenberger, Bernd & Rümmele, Marian, 2022. "Using Distribution Regression Difference-in-Differences to Evaluate the Effects of a Minimum Wage Introduction on the Distribution of Hourly Wages and Hours Worked," IZA Discussion Papers 15534, Institute of Labor Economics (IZA).
    4. Wang, Lijian & Béland, Daniel & Zhang, Sifeng, 2014. "Pension fairness in China," China Economic Review, Elsevier, vol. 28(C), pages 25-36.
    5. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.
    6. Kawakubo, Yuki & Kobayashi, Genya, 2023. "Small area estimation of general finite-population parameters based on grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).

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