Some remarks on Lorenz ordering-preserving functionals |
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Authors: | Lucio Bertoli-Barsotti |
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Affiliation: | 1. Departimento di Statistica e Matematica Applicata alle Scienze Umane Diego de Castro, University of Torino, Italy, Piazza Arbarello 8, I-10122, Torino, Italy
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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. |
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