Typological Grouping Based on Decomposition of Probability Distributions Mixtures

Abstract

A mixture of probability distributions is a mathematical model that allows to describe heterogeneous data. The task of separating mixtures or decomposition is the task of estimating the unknown parameters of miscible distributions. Despite the adequacy of the description of heterogeneous data, the decomposition of mixtures is a separate problem, due to the large number of parameters to be evaluated. The article carries out historical periodization,systematization, and a critical comparative analysis of existing methods and algorithms for decomposition of mixtures of probability distributions, identifies the possibilities and limitations of their application for the analysis of real populations. Based on existing algorithms, a method for separating mixtures of an arbitrary known number of probability distributions and a further typological grouping of real socio-economic aggregates is proposed. Unlike existing methods, a method for calculating threshold values to determine the boundaries of types and the number of components of the mixture, in cases where it is unknown, is proposed. Based on the proposed methodology, a typology of the subjects of the Russian Federation by the level of unemployment in the Russian Federation is carried out.