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On Zenga and Bonferroni curves

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  • Barry Arnold

Abstract

Three alternative inequality curves are considered as competitors of the classical Lorenz curve as descriptors of income inequality. The Bonferroni curve and the Zenga-07 curve appear to be essentially equivalent to the Lorenz curve. They each determine the parent distribution up to scale factor, and they each yield an inequality partial order that is equivalent to the Lorenz order. The Zenga-84 curve is more problematic. It is scale invariant, but it is possible that different distributions can have the same Zenga-84 curve. Thus it fails to identify the parent distribution up to a scale factor. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Barry Arnold, 2015. "On Zenga and Bonferroni curves," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 25-30, April.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:1:p:25-30
    DOI: 10.1007/s40300-014-0050-3
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    References listed on IDEAS

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    1. Gaetano Pietra, 2014. "On the relationships between variability indices (Note I)," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 5-16, April.
    2. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
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    Cited by:

    1. Francesca Battisti & Francesco Porro, 2023. "A multi-decomposition of Zenga-84 inequality index: an application to the disparity in CO $$_2$$ 2 emissions in European countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 957-981, September.
    2. Francesco Porro & Michele Zenga, 2020. "Decomposition by subpopulations of the Zenga-84 inequality curve and the related index $$\zeta $$ζ: an application to 2014 Bank of Italy survey," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 187-207, March.
    3. Zahra Behdani & Gholam Reza Mohtashami Borzadaran & Bahram Sadeghpour Gildeh, 2020. "Some properties of double truncated distributions and their application in view of income inequality," Computational Statistics, Springer, vol. 35(1), pages 359-378, March.

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