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Increasing concave orderings of linear combinations of order statistics with applications to social welfare

Author

Listed:
  • Antonia Castaño-Martínez

    (University of Cádiz)

  • Gema Pigueiras

    (University of Cádiz)

  • Georgios Psarrakos

    (University of Piraeus)

  • Miguel A. Sordo

    (University of Cádiz)

Abstract

We provide in this paper sufficient conditions for comparing, in terms of the increasing concave order, some income random variables based on linear combinations of order statistics that are relevant in the framework of social welfare. The random variables under study are weighted average incomes of the poorest and, for some particular weights, their expectations are welfare measures whose integral representations are weighted areas underneath Bonferroni curves.

Suggested Citation

  • Antonia Castaño-Martínez & Gema Pigueiras & Georgios Psarrakos & Miguel A. Sordo, 2020. "Increasing concave orderings of linear combinations of order statistics with applications to social welfare," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 699-712, August.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:6:d:10.1007_s00184-019-00754-1
    DOI: 10.1007/s00184-019-00754-1
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    References listed on IDEAS

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    1. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    2. Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
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    More about this item

    Keywords

    Increasing concave order; Generalized Lorenz order; Welfare measurement; Order statistics;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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