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Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View

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  • Ricardas Zitikis

    () (Department of Statistical and Actuarial Sciences, The University of Western Ontario, AND Laboratory for Research in Statistics and Probability, Carleton University,)

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    Abstract

    A number of indices of economic inequality have been proposed in the literature. Their constructions are based on various econometric motives and justifications such as axioms of fairness. In this paper we analize the indices stepping slightly aside from their econometric meanings and adopting a mathematical approach that treats the indices as distances – in some functional spaces – between the egalitarian and actual Lorenz curves. More specifically, starting with, and being guided by, the econometric definitions of various indices, we modify the indices in such a way that the resulting ones become natural from the mathematical point of view. It turns out that some of the new “mathematical” indices coincide with the corresponding well known “econometric” ones, some appear to be only asymptotically equivalent, and some turn out to have different asymptotic behaviour when the sample size indefinitely increases.

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    File URL: http://www.repad.org/ca/on/lrsp/TRS366.pdf
    File Function: First version, 2002
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    Bibliographic Info

    Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS366.

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    Length: 14 pages
    Date of creation: 25 Jul 2002
    Date of revision:
    Handle: RePEc:pqs:wpaper:0092005

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    Keywords: Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.;

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