Some remarks on Lorenz ordering-preserving functionals

Lucio Bertoli-Barsotti ()
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Lucio Bertoli-Barsotti: University of Torino, Italy

Statistical Methods & Applications, 2001, vol. 10, issue 1, No 9, 99-112

Abstract: 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.

Keywords: Lorenz; ordering; continuous; majorization; stochastic; dominance; isotonicity; Schur-convexity; ZengaZ; concentration; index (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/BF02511642

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