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.
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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.
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Castaño-Martínez, A., Pigueiras, G., Psarrakos, G. et al. Increasing concave orderings of linear combinations of order statistics with applications to social welfare. Metrika 83, 699–712 (2020). https://doi.org/10.1007/s00184-019-00754-1
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DOI: https://doi.org/10.1007/s00184-019-00754-1