Modeling Human Development Index Using Finite Mixtures of Distributions

Abstract

The Human Development Index (HDI) measures development of a country which was designed by the United Nations Development Programme (UNDP). Since the values of HDI for different countries show differences according to the development of a country, the distribution of HDI may have one more mode, thick tail or skewness. Therefore, we can use mixtures of distributions to model the HDI data set to handle modality, heavy-tailedness and/or skewness. In this paper, we propose finite mixtures of distributions to model the data from the HDI report 2015 for 186 countries. We give the basic scheme of the maximum likelihood (ML) estimation using Expectation-Maximization (EM) algorithm for finite mixture model. To obtain best model for HDI data set, we first find the appropriate cluster number using model-based clustering. Then, we use the finite mixture models obtained from some symmetric and/or heavy-tailed and skew and/or heavy-tailed distributions to find the best model for HDI data set.