The Use Of Finite Mixtures Of Lognormal Distributions In The Modeling Of Incomes In The Czech Republic

Abstract

Finite mixtures of probability distributions are used for the modeling of probability distributions of incomes. These distributions are typically non-homogenous, heavy tailed and positively skewed. In the text a net annual incomes per capita of the Czech households in 2004 and 2008 are analysed. The finite mixtures of lognormal distributions are fitted into data from the survey Results of the Living Conditions Survey (a national module of the European Union Statistics on Income and Living Conditions (EU-SILC)) that has been held by the Czech Statistical Office since 2005. Firstly, the components with known group membership are formed according to the education of a head of a household (factor with 5 levels) and number of children (2 levels factor children yes/no and more detailed 5 levels factor) in the household. Secondly, data are divided into groups with unknown group membership in order to obtain the best possible fit. In this case 1 to 5 components in the mixture are used. All models fitted into data are compared with the use of Akaike criterion.