Politická ekonomie 2013, 61(3):356-372 | DOI: 10.18267/j.polek.902

Použití konečných směsí logaritmicko-normálních rozdělení pro modelování příjmů českých domácností

Ivana Malá
Vysoká škola ekonomická v Praze.

The Use of Finite Mixtures of Lognormal Distribution for the Modelling of Household Income Distributions in the Czech Republic

In the text finite mixtures of lognormal distributions are used for the modelling of net annual income per capita and equivalized income of the Czech households (in CZK) in 2004-2010. The development of distribution of number of members of households is analysed and the characteristics of standardized units according to EU and OECD methodologies are given. Data from the survey EU-SILC organized by the Czech Statistical Office from 2005-2011 (dealing with incomes from 2004-2010) are used for the analysis. Models (with incomplete data) with two to four artificial components are used in order to fit the distribution of incomes; the development of their characteristics is shown. All estimates in the text are maximum likelihood estimates, EM algorithm in the program R is used for the optimalization. Models are compared with the use of Akaike criterion.

Keywords: finite mixture of distributions, income distribution, income inequality, Gini coefficient, EM algorithm
JEL classification: C13, C51, O15

Published: June 1, 2013  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Malá, I. (2013). The Use of Finite Mixtures of Lognormal Distribution for the Modelling of Household Income Distributions in the Czech Republic. Politická ekonomie, 61(3), 356-372. doi: 10.18267/j.polek.902
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. BARTOŠOVÁ, J. 2009. Analysis and Modelling of Financial Power of Czech Households. Bratislava 03. 02. 2009 - 06. 02. 2009. In 8th International Conference APLIMAT 2009. Bratislava: Slovak University of Technology, pp. 717-722.
    2. BARTOŠOVÁ, J.; BÍNA, V. 2009. Modelling of Income Distribution of Czech Households in Years 1996 - 2005. Acta Oeconomica Pragensia. Vol. 17, No. 4, pp. 3-18. Go to original source...
    3. BÍLKOVÁ, D. 2012. Recent Development of the Wage and Income Distribution in the Czech Republic. Prague Economic Papers, Vol. 21, No. 2, pp. 233-250. Go to original source...
    4. DAGUM, C. A 2008. New Model of Personal Income Distribution: Specification and Estimation, In Modeling Income Distributions and Lorenz Curves, Economic Studies in Equality, Social Exclusion and Well-Being, Vol. 5, pp. 3-25. Go to original source...
    5. FLACHAIRE E.; NUNEZ O. 2007. Estimation of the Income Distribution and Detection of Subpopulations: an Explanatory Model. Computational Statistics & Data Analysis. 2007. Vol. 51, No.7, pp. 3368-3380. Go to original source...
    6. HEBÁK, P.; HUSTOPECKÝ, J.; PECÁKOVÁ, I.; PLAŠIL, M.; PRŮŠA, P.; VLACH P.; SVOBODOVÁ, A. A. 2007. Vícerozměrné statistické metody [3]. 2. vyd. Praha: Informatorium, 2007.
    7. KLEIBER, C.; KOTZ, S. 2003. Statistical Size Distributions in Economics and Actuarial Sciences. New York: Wiley-Interscience, 2003. Go to original source...
    8. KLEIBER, C. A. 2007. Guide to the Dagum Distributions. Working paper 23/07, Wirtschaftswissenechaftliches Zentrum (WWZ) der Univeritat Basel, Dostupné na http://wwz.unibas.ch/uploads/tx_x4epublication/23_07.pdf.
    9. MALÁ, I. 2011. Distribution of Incomes Per Capita of the Czech Households from 2005 to 2008. Bratislava 01.02.2011 - 04.02.2011. In Aplimat 2011 [CD-ROM]. Bratislava: Slovak University of Technology, pp. 1583-1588.
    10. MALÁ, I. 2012. Použití konečných směsí pro modelování příjmových rozdělení. Acta Oeconomica Pragensia, Vol. 20, No. 4, pp. 26-39. Go to original source...
    11. MCDONALD, J. B. 1984. Some Generalized Functions for the Size Distributions of Income. Econometrica, Vol. 52, pp. 647-663. Go to original source...
    12. MCDONALD, J. B.; XU, Y. J. 1995. A Generalization of the Beta Distribution with Applications. Journal of Econometrics, Vol. 66, No. 6, pp. 133-152. Go to original source...
    13. MCLACHLAN, G. J.; PEEL, D. 2000. Finite Mixture Models. New York: Wiley series in Probability and Mathematical Statistics: Applied Probability and Statistics Section. Go to original source...
    14. MILANOVIC, B. 2002. True World Income Distribution, 1988 and 1993: First Calculation Based on Household Surveys Alone. The Economic Journal, 2002. Vol. 112, pp. 51-92. Go to original source...
    15. MORLEY, S. A. 1981. The Effect of Changes in the Population on Several Measures of Income Distribution. The American Economic Review, Vol. 71, No. 3, pp. 285-294.
    16. PACÁKOVÁ, V.; SIPKOVÁ, L. 2007. Generalized Lambda Distributions of Households Incomes. E + M Ekonomie a Management, Vol.10, No.1, pp. 98-107.
    17. PITTAU, M. G.; ZELLI, R. 2006. Empirical Evidence of Income Dynamics across EU Regions. Journal of Applied Econometrics, Vol. 21, No. 5, pp. 605-628. Go to original source...
    18. PRIETO-ALAIZ, M.; VICTORIA-FESER, M. P. 1996. Modelling Income Distribution in Spain: A Robust Parametric Approach. STICERD - Distributional Analysis Research Programme Papers 20, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. YOUNG, Y. 2011. The Gini Coefficient for a Mixture of Ln-Normal Populations, Working Paper LSE, London. Dostupné na http://personal.lse.ac.uk/YoungA/MixtureGini.pdf.
    20. WU, X.; PERLOFF, J. M. 2005. China's Income Distribution, 1985-2001. The Review of Economics and Statistics, Vol. 87, No. 4, pp. 763-775.
    21. CZSO. Czech Statistical Office. Dostupné na www.czso.cz.
    22. RPROGRAM. R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2012. Dostupné na http://www.R-project.org/.
    23. MIXTOOLS. Tatiana Benaglia, Didier Chauveau, David R. Hunter, Derek Young. mixtools: An R Package for Analyzing Finite Mixture Models. Journal of Statistical Software, 32(6), 1-29. 2009. Dostupné na http://www.jstatsoft.org/v32/i06/. Go to original source...

    This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY NC ND 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content