C46 - Specific Distributions; Specific StatisticsReturn

The equivalised total net annual incomes of the Czech households (in CZK) in 2007-2010 are analysed in the text. The set of all households is very nonhomogeneous (with respect to incomes) and the aim of the analysis is to determine more homogeneous subsets (components) and to describe the distribution of incomes in these components. The components are supposed to be artificial, the membership of households in components is not known (or observable). A multivariate mixture of normal distributions (four dimensional component distributions) is used to describe a vector of logarithms of incomes, models with 2 to 9 components are fitted. Maximum likelihood estimates of unknown parameters were found with the use of EM algorithm. Akaike information criterion was used (accompanied by bootstraped test) and models with 3 or 4 components were selected to be acceptable for the description of distribution of incomes. Cluster analysis was performed in order to classify households into components and good performance of the model was found.