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

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.