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The Gini coefficient and negative income: A probabilistic approach

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  • Karim Kilani

    (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM] - HESAM - HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université)

Abstract

This paper discusses the Gini index when a mass of individuals in the population sharing the wealth suffers a loss. This question has been addressed in the statistical framework while here it is treated from a probabilistic point of view, which allows us to be as exhaustive as possible. The assumptions are the most general ones on probability distributions. We determine a condition on the Lorenz function that generates a Gini index that exceeds unity. We construct an adjusted Gini index, i.e. one that remains within limits between zero and one, according to a method advocated in the statistical framework. After having recovered the recommended index in the statistical case, we apply the method to continuous distributions, namely the uniform distribution and the generalized Pareto distribution, thus showing the operability of the method.

Suggested Citation

  • Karim Kilani, 2022. "The Gini coefficient and negative income: A probabilistic approach," Working Papers hal-03911502, HAL.
    • Handle: RePEc:hal:wpaper:hal-03911502
    Note: View the original document on HAL open archive server: https://hal.science/hal-03911502
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    References listed on IDEAS

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    1. Chen, Chau-Nan & Tsaur, Tien-Wang & Rhai, Tong-Shieng, 1982. "The Gini Coefficient and Negative Income," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 473-478, November.
    2. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Adjusted Gini index; Lorenz function; Negative income; Quantile function JEL classification. C43;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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