IDEAS home Printed from
   My bibliography  Save this article

The Use of Finite Mixtures of Lognormal Distribution for the Modelling of Income Distributions


  • Ivana Malá


In the text finite mixtures of lognormal distributions are used for the modelling of net annual per capita income of the Czech households in Czech crowns in 2004?2008. All the households are divided into subgroups with observed group membership according to the attained education of the head of a household (a factor with five levels: basic, secondary, complete secondary, bachelor, magister education), the existence of children in the household (a factor with two levels: children yes or no) and the number of children (a factor with five levels: 0?3, more than 3 children). Then, models with incomplete data (unobserved component membership) were used for 2?5 components. All the estimates in the text are maximum likelihood estimates; explicit formulas exist for the complete data models; an EM algorithm for normal mixtures incorporated in the flexmix package in R was used for the incomplete data models. The models are compared with the use of the Akaike criterion. Maximum likelihood estimates of mixing proportions, expected values and standard deviations of the components are given and their development in the five-year period analysed is discussed. The program R was used for all the computations.

Suggested Citation

  • Ivana Malá, 2012. "The Use of Finite Mixtures of Lognormal Distribution for the Modelling of Income Distributions," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2012(4), pages 26-39.
  • Handle: RePEc:prg:jnlaop:v:2012:y:2012:i:4:id:373:p:26-39

    Download full text from publisher

    File URL:
    Download Restriction: free of charge

    File URL:
    Download Restriction: free of charge

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    2. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    3. Grün, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    4. Flachaire, Emmanuel & Núñez, Olivier, 2003. "Estimation of income distribution and detection of subpopulations: an explanatory model," DES - Working Papers. Statistics and Econometrics. WS ws030201, Universidad Carlos III de Madrid. Departamento de Estadística.
    Full references (including those not matched with items on IDEAS)

    More about this item


    income distribution; finite mixture of distributions; lognormal distribution;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:prg:jnlaop:v:2012:y:2012:i:4:id:373:p:26-39. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Frantisek Sokolovsky). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.