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κ-generalized statistics in personal income distribution

  • F. Clementi


  • M. Gallegati
  • G. Kaniadakis

Starting from the generalized exponential function $\exp_{\kappa}(x)=(\sqrt{1+\kappa^{2}x^{2}}+\kappa x)^{1/\kappa}$ , with exp 0 (x)=exp (x), proposed in reference [G. Kaniadakis, Physica A 296, 405 (2001)], the survival function P >(x)=exp κ (-βx α ), where x∈R +, α,β>0, and $\kappa\in[0,1)$ , is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function P > 0 (x)=exp (-βx α ) to which reduces as κ approaches zero behaving in very different way in the x→0 and x→∞ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law P >(x)∼(2βκ) -1/κ x-α/κ . This makes the κ-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

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Article provided by Springer in its journal The European Physical Journal B.

Volume (Year): 57 (2007)
Issue (Month): 2 (05)
Pages: 187-193

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Handle: RePEc:spr:eurphb:v:57:y:2007:i:2:p:187-193
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  1. Andrea Brandolini, 1999. "The Distribution of Personal Income in Post-War Italy: Source Description, Data Quality, and the Time Pattern of Income Inequality," Giornale degli Economisti, GDE (Giornale degli Economisti e Annali di Economia), Bocconi University, vol. 58(2), pages 183-239, September.
  2. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, EconWPA.
  3. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, 09.
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