# κ-generalized statistics in personal income distribution

## Author Info

• F. Clementi

()

• M. Gallegati
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## Abstract

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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## Bibliographic Info

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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Web page: http://www.springer.com/economics/journal/10051

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## Related research

Keywords: 02.50.Ng Distribution theory and Monte Carlo studies; 02.60.Ed Interpolation; curve fitting; 89.65.Gh Economics; econophysics; financial markets; business and management;

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## References

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1. G. Willis & J. 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," Papers cond-mat/0406694, arXiv.org.
2. Brandolini, A., 1999. "The Distribution of Personal Income in Post-War Italy: Source Description, Date Quality, and the Time Pattern of Income Inequality," Papers, Banca Italia - Servizio di Studi 350, Banca Italia - Servizio di Studi.
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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## Citations

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Cited by:
1. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
2. F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787, arXiv.org, revised Dec 2012.
3. Masato Okamoto, 2012. "Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation," Economics Bulletin, AccessEcon, vol. 32(4), pages 2969-2982.
4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
5. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
6. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.

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