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

By Gianni Betti, Achille Lemmi

This impressive collection from a few of today’s best distributional analysts presents an outline a variety of financial, statistical and sociological relationships which were unfolded for clinical research by means of the paintings of 2 turn-of-the-20th-century economists: C. Gini and M. O. Lorenz.

The authors contain such figues as Barry Arnold and Frank Cowell and the ensuing e-book merits its position at the bookshelf of significant mathematical economists everywhere.

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Iv) X ≤L Y if c ′ X ≤L c ′ Y ∀c ∈ ℜm+ . (v) X ≤L Y if Xᐍ ≤L Yᐍ, ᐍ = 1, 2, . , m. 1 ΂ ΂ ΃΃ ΂ ΂ ΃΃ 2 3 4 Evidently the last three of these orderings are related in the sense that (iii) ⇒ (iv) ⇒ (v). Definition (v) could be labeled marginal Lorenz ordering. Our Lorenz zonoid order, (i), is actually equivalent to ordering (iii). Thus zonoid ordering implies but is not implied by exchange rate Lorenz ordering (or positive combinations Lorenz ordering in the terminology of Joe and Verducci 1992). Adding to its list of aliases, Mosler (2002) calls it the price Lorenz order.

B) (Hardy, Littlewood and Polya 1934). If x ՞ y then there exists a finite set of matrices in ᐀n, say T1, T2 , . . , Tm such that x = T1 T2. . Tm y (in fact m will be ≤ n − 1 here). 2(b) it is possible to verify Schur convexity of a function by considering only the effect of changes in the first two coordinates. Thus a differentiable function g : In → ℜ, where I is an interval, is Schur convex if: (i) g is a symmetric function of x1, x2, . . , xn (ii) for every x ∈ In ∂ ΂∂x (x1 − x2) g(x) − 1 ∂ g(x) ≥ 0.

E. Littlewood and G. Polya (1934). , London: Cambridge University Press. L. J. Slottje (2003) ‘Inequality aversion and the natural rate of subjective inequality’, Journal of Public Economics 87: 1061–90. Lemmi A. A. Cowell, Estimation of Inequality Indices’, in Editors’ introduction 11 Silber, J. ), Handbook on Income Inequality Measurement, Kluwer Academic Publishers: Boston/Dordrecht/London, pp. 286–289. O. (1905). ‘Methods of measuring concentration of wealth’, Journal of the American Statistical Association, 9: 209–219.

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