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The Gini coefficient and discontinuity

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  • Jens Peter Kristensen

Abstract

This article reveals a discontinuity in the mapping from a Lorenz curve to the associated cumulative distribution function. The problem is of a mathematical nature—based on an analysis of the transformation between the distribution function of a bound random variable and its Lorenz curve. It will be proven that the transformation from a normalized income distribution to its Lorenz curve is a continuous bijection with respect to the $${L^q}$$Lq ([0,1])-metric—for every q ≥ 1. The inverse transformation, however, is not continuous for any q ≥ 1. This implies a more careful attitude when interpreting the value of a Gini coefficient. A further problem is that if you have estimated a Lorenz curve from empirical data,then you cannot trust that the associated distribution is a good estimate of the true income distribution.

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  • Jens Peter Kristensen, 2022. "The Gini coefficient and discontinuity," Cogent Economics & Finance, Taylor & Francis Journals, vol. 10(1), pages 2072451-207, December.
    • Handle: RePEc:taf:oaefxx:v:10:y:2022:i:1:p:2072451
    DOI: 10.1080/23322039.2022.2072451
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    Cited by:

    1. Fazley K. Siddiq & Halyna Klymentieva & Taylor J. C. Lee, 2023. "Applying the Lorenz Curve and Gini Coefficient to Measure the Population Distribution," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 29(3), pages 177-192, August.

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