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A generalized statistical model for the size distribution of wealth


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


In a recent paper in this journal [J. Stat. Mech. (2009) P02037] we proposed a new, physically motivated, distribution function for modeling individual incomes having its roots in the framework of the k-generalized statistical mechanics. The performance of the k-generalized distribution was checked against real data on personal income for the United States in 2003. In this paper we extend our previous model so as to be able to account for the distribution of wealth. Probabilistic functions and inequality measures of this generalized model for wealth distribution are obtained in closed form. In order to check the validity of the proposed model, we analyze the U.S. household wealth distributions from 1984 to 2009 and conclude an excellent agreement with the data that is superior to any other model already known in the literature.

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  • F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787,, revised Dec 2012.
  • Handle: RePEc:arx:papers:1209.4787

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    References listed on IDEAS

    1. James B. Davies & Susanna Sandström & Anthony Shorrocks & Edward Wolff, 2009. "The global pattern of household wealth," Journal of International Development, John Wiley & Sons, Ltd., vol. 21(8), pages 1111-1124.
    2. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2012. "A new model of income distribution: the κ-generalized distribution," Journal of Economics, Springer, vol. 105(1), pages 63-91, January.
    3. Clementi, F. & Di Matteo, T. & Gallegati, M. & Kaniadakis, G., 2008. "The κ-generalized distribution: A new descriptive model for the size distribution of incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3201-3208.
    4. Jenkins, Stephen P. & Jantti, Markus, 2005. "Methods for summarizing and comparing wealth distributions," ISER Working Paper Series 2005-05, Institute for Social and Economic Research.
    5. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    6. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    7. Richard T. Curtin & Thomas Juster & James N. Morgan, 1989. "Survey Estimates of Wealth: An Assessment of Quality," NBER Chapters,in: The Measurement of Saving, Investment, and Wealth, pages 473-552 National Bureau of Economic Research, Inc.
    8. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075,, revised Feb 2009.
    9. Stiglitz, Joseph E, 1969. "Distribution of Income and Wealth among Individuals," Econometrica, Econometric Society, vol. 37(3), pages 382-397, July.
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    11. Kleiber, Christian, 2007. "A Guide to the Dagum Distributions," Working papers 2007/23, Faculty of Business and Economics - University of Basel.
    12. Martin Biewen & Stephen Jenkins, 2005. "A framework for the decomposition of poverty differences with an application to poverty differences between countries," Empirical Economics, Springer, vol. 30(2), pages 331-358, September.
    13. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
    14. Robert E. Lipsey & Helen Stone Tice, 1989. "The Measurement of Saving, Investment, and Wealth," NBER Books, National Bureau of Economic Research, Inc, number lips89-1, January.
    15. Claudio Quintano & Antonella D'Agostino, 2006. "Studying Inequality In Income Distribution Of Single-Person Households In Four Developed Countries," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 52(4), pages 525-546, December.
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    17. Rajaonarison, Dominique & Bolduc, Denis & Jayet, Hubert, 2005. "The K-deformed multinomial logit model," Economics Letters, Elsevier, vol. 86(1), pages 13-20, January.
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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. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    3. repec:bla:revinw:v:63:y:2017:i:4:p:867-880 is not listed on IDEAS
    4. F. Clementi & M. Gallegati, 2016. "New economic windows on income and wealth: The k-generalized family of distributions," Papers 1608.06076,

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