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A k-generalized statistical mechanics approach to income analysis


  • F. Clementi
  • M. Gallegati
  • G. Kaniadakis


This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of k-generalized statistics, is derived that is particularly suitable to describe the whole spectrum of incomes, from the low-middle income region up to the high-income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters reveals very powerful.

Suggested Citation

  • F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075,, revised Feb 2009.
  • Handle: RePEc:arx:papers:0902.0075

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    Cited by:

    1. Calderín-Ojeda, Enrique & Azpitarte, Francisco & Gómez-Déniz, Emilio, 2016. "Modelling income data using two extensions of the exponential distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 756-766.
    2. Maria Letizia Bertotti & Giovanni Modanese, 2015. "Economic inequality and mobility in kinetic models for social sciences," Papers 1504.03232,
    3. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.
    4. Elvis Oltean, 2016. "Modelling income, wealth, and expenditure data by use of Econophysics," Papers 1603.08383,
    5. repec:aes:jsesro:v:6:y:2017:i:1:p:1-15 is not listed on IDEAS
    6. Masato Okamoto, 2013. "Extension of the ?-generalized distribution: new four-parameter models for the size distribution of income and consumption," LIS Working papers 600, LIS Cross-National Data Center in Luxembourg.
    7. F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787,, revised Dec 2012.
    8. 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.
    9. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    10. 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.

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