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

  • Antonia Castaño-Martínez
  • Gema Pigueiras
  • Georgios Psarrakos
  • Miguel A. SordoEmail author
Article
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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.

Keywords

Increasing concave order Generalized Lorenz order Welfare measurement Order statistics 

JEL Classification

G220 

Notes

Acknowledgements

We thank the associated editor and two anonymous reviewers for constructive and helpful comments. M.A.S and G.P acknowledge support received from the Ministerio de Economía y Competitividad under Grant MTM2017-89577-P. A.C.M. acknowledges support received from the Ministerio de Economía y Competitividad under Grant MTM2016-74983-C2-2-R.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of CádizCádizSpain
  2. 2.Department of Statistics and Insurance ScienceUniversity of PiraeusPiraeusGreece

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