Probabilistic Mixtures in Measurements of Interterritorial Differentiation

The article summarizes research results of the study on the problem of assessing the differentiation level of socio-economic development of territorial units of the Russian Federation. The authors propose an approach to measuring differentiation using mixtures of probability distributions. This technique was developed and tested on real data that allows one to determine the presence or absence of interregional differentiation. The research hypothesis, that interterritorial differentiation is estimated by a specic statistical indicator selected based on a content, qualitative analysis, served as a theoretical platform of this methodology. Differentiation is practically absent if the entire statistical population is described by a single law of probability distribution. If the statistical population is described by a mixture of probability distributions, then one should expect the presence of a signicant level of differentiation by the considered indicator. In mathematical statistics, the problem of separating a mixture of probability distributions (estimating parameters of distribution densities and weighting coefficients) is traditionally solved using several similar methods. For example, the expectation-maximization (EM) algorithm, median modications of the EM-algorithm, SEM-algorithm, taking into account the specics of the selected object (constituent entities of the Russian Federation a small sample). To solve this problem, the authors used the SEM algorithm. As the information base of the empirical study, official statistics were used (open data from the Federal State Statistics Service). The typologies of the constituent entities of the Russian Federation were identied based on two characteristics within 2005-2017-time interval. The rst one being the level of violence (using the “homicide rate” indicator the number of homicides and attempted murders per 1 population). And second average per capita income, which made it possible, among other things, to additionally test the hypothesis of the traditional use of differentiation trends in the level of violence as an indicator of economic inequality. According to the authors, the results of this study can be used as instrumental and informational support for managerial decisions aimed at regulating the differentiation of Russian regions by the level of violence and economic inequality.