By Gianni Betti, Achille Lemmi

ISBN-10: 0203927923

ISBN-13: 9780203927922

ISBN-10: 0415443377

ISBN-13: 9780415443371

This impressive collection from a few of today’s prime distributional analysts offers an summary quite a lot of monetary, statistical and sociological relationships which were spread out for medical examine by means of the paintings of 2 turn-of-the-20th-century economists: C. Gini and M. O. Lorenz.

The authors comprise such figues as Barry Arnold and Frank Cowell and the ensuing ebook merits its position at the bookshelf of great mathematical economists everywhere.

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**Extra info for Advances on Income Inequality and Concentration Measures**

**Sample text**

As a rule of thumb, if a problem deals with vectors in ℜ+n and if the extremal solution to that problem is a vector of the form (c, c, . , c) then we should look for the potential role of some Schur convex function and be on the lookout for a Lorenz ordering (or majorization) interpretation of the phenomenon in question. A more extensive collection of such examples may be found in Arnold (2007) (described speciﬁcally in terms of majorization), but it is hoped that the small selection presented below will serve to indicate some of the possibilities and will encourage readers to be on the lookout for more places for Max Lorenz’s ordering to play a fruitful role.

Schur, I. (1923). ‘Uber eine Klasse von Mittel bildungen mit Arwendungen die Determinanten-Theorie Sitzungsber’, Berlin Math. Gesellschaft 23: 9–20. Taguchi, T. (1972). ‘On the two-dimensional concentration surface and extensions of concentration coeﬃcient and Pareto distribution to the two-dimensional case (on an application of diﬀerential geometric methods to statistical analysis). ’, Annals of the Institute of Statistical Mathematics, 24: 355–381. 3 Gini, deprivation and complaints Frank A. 1 Introduction The early contributions of Gini and Lorenz have shaped the way the whole subject of income-distribution analysis has developed (Gini 1912, Lorenz 1905).

Ii) X is an averaging of Y in the sense that there exist jointly distributed random variables Y′, Z′ such that Y =d Y′ and X =d E(Y′ | Z′). (iii) E(h(X)) ≤ E(h(Y)) for every continuous convex function h : ℜ → ℜ. (iv) E((X − c)+) ≤ E((Y − c)+), ∀c ∈ ℜ+. 7 Extremal patterns Among the set of vectors x ∈ ℜ+n with Α n i=1 xi = c > 0, the extremal cases with respect to majorization are of the form (c/n, c/n, . , c/n) and (0, 0, . ,0) corresponding, in income terms, to distributions in which, respectively, the wealth is evenly distributed or is all in the hands of one individual.

### Advances on Income Inequality and Concentration Measures by Gianni Betti, Achille Lemmi

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