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Egghe's construction of Lorenz curves resolved.

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Title: Egghe's construction of Lorenz curves resolved.
Authors: Burrell, Quentin L.1 q.burrell@ibs.ac.im
Source: Journal of the American Society for Information Science & Technology. Nov2007, Vol. 58 Issue 13, p2157-2159. 3p. 2 Graphs.
Subjects: Lorenz curve, Econometric models, Concave functions, Real variables, Mathematical models, Information science, Probability measures, Density functionals, Random variables
Abstract: In a recent article (Burrell, 2006), the author pointed out that the version of Lorenz concentration theory presented by Egghe (2005a, 2005b) does not conform to the classical statistical/econometric approach. Rousseau (2007) asserts confusion on our part and a failure to grasp Egghe's construction, even though we simply reported what Egghe stated. Here the author shows that Egghe's construction rather than “including the standard case,” as claimed by Rousseau, actually leads to the Leimkuhler curve of the dual function, in the sense of Egghe. (Note that here we distinguish between the Lorenz curve, a convex form arising from ranking from smallest to largest, and the Leimkuhler curve, a concave form arising from ranking from largest to smallest. The two presentations are equivalent. See Burrell, 1991, 2005; Rousseau, 2007.) [ABSTRACT FROM AUTHOR]
Copyright of Journal of the American Society for Information Science & Technology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Egghe's construction of Lorenz curves resolved.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+the+American+Society+for+Information+Science+%26+Technology%22">Journal of the American Society for Information Science & Technology</searchLink>. Nov2007, Vol. 58 Issue 13, p2157-2159. 3p. 2 Graphs.
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  Data: <searchLink fieldCode="DE" term="%22Lorenz+curve%22">Lorenz curve</searchLink><br /><searchLink fieldCode="DE" term="%22Econometric+models%22">Econometric models</searchLink><br /><searchLink fieldCode="DE" term="%22Concave+functions%22">Concave functions</searchLink><br /><searchLink fieldCode="DE" term="%22Real+variables%22">Real variables</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Information+science%22">Information science</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Density+functionals%22">Density functionals</searchLink><br /><searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In a recent article (Burrell, 2006), the author pointed out that the version of Lorenz concentration theory presented by Egghe (2005a, 2005b) does not conform to the classical statistical/econometric approach. Rousseau (2007) asserts confusion on our part and a failure to grasp Egghe's construction, even though we simply reported what Egghe stated. Here the author shows that Egghe's construction rather than “including the standard case,” as claimed by Rousseau, actually leads to the Leimkuhler curve of the dual function, in the sense of Egghe. (Note that here we distinguish between the Lorenz curve, a convex form arising from ranking from smallest to largest, and the Leimkuhler curve, a concave form arising from ranking from largest to smallest. The two presentations are equivalent. See Burrell, 1991, 2005; Rousseau, 2007.) [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of the American Society for Information Science & Technology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/asi.20674
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 3
        StartPage: 2157
    Subjects:
      – SubjectFull: Lorenz curve
        Type: general
      – SubjectFull: Econometric models
        Type: general
      – SubjectFull: Concave functions
        Type: general
      – SubjectFull: Real variables
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Information science
        Type: general
      – SubjectFull: Probability measures
        Type: general
      – SubjectFull: Density functionals
        Type: general
      – SubjectFull: Random variables
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      – TitleFull: Egghe's construction of Lorenz curves resolved.
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            – D: 01
              M: 11
              Text: Nov2007
              Type: published
              Y: 2007
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            – TitleFull: Journal of the American Society for Information Science & Technology
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