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

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  • Ivana Malá
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    Abstract

    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.

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    Bibliographic Info

    Article provided by University of Economics, Prague in its journal Acta Oeconomica Pragensia.

    Volume (Year): 2012 (2012)
    Issue (Month): 4 ()
    Pages: 26-39

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    Handle: RePEc:prg:jnlaop:v:2012:y:2012:i:4:id:373:p:26-39

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    Related research

    Keywords: lognormal distribution; income distribution; finite mixture of distributions;

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    References

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    1. Emmanuel Flachaire & Olivier G. Núñez, 2003. "Estimation Of Income Distribution And Detection Of Subpopulations: An Explanatory Model," Statistics and Econometrics Working Papers ws030201, Universidad Carlos III, Departamento de Estadística y Econometría.
    2. Bettina Grün & Friedrich Leisch, . "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, American Statistical Association, vol. 28(i04).
    3. 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.
    4. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
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