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Some remarks on Lorenz ordering-preserving functionals

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  • Lucio Bertoli-Barsotti

    (University of Torino, Italy)

Abstract

Basing on two well-known characterization results on stochastic dominance and continuous majorization relation, the ordering-preserving property-with respect to Lorenz ordering-is deduced for a wide class of families of functionals on a class of distributions. As a consequence the isotonicity ofZ Zenga concentration index is deduced as an immediate application of a characterization result, in particular of the first degree stochastic dominance relation. Moreover it is also shown that a classical inequality by Fan and Lorenz is a basic reference for the determination of a wide class of Lorenz ordering-preserving functionals. Isotonicity ofZ could also be seen as a straighforward application of Fan and Lorenz inequality.

Suggested Citation

  • Lucio Bertoli-Barsotti, 2001. "Some remarks on Lorenz ordering-preserving functionals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 99-112, January.
    • Handle: RePEc:spr:stmapp:v:10:y:2001:i:1:d:10.1007_bf02511642
    DOI: 10.1007/BF02511642
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    References listed on IDEAS

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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.

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