Small and Medium-Sized Enterprises in the Russian Federation: Regularities of Spatial Distribution

Small and medium-sized business enterprises (SMEs) have been operating in the Russian Federation since 1991. The study is devoted to the development of methods and tools for assessing the current structure of production volumes, the number of employees and the number of small and medium enterprises, as well as individual entrepreneurs through: economic and mathematical modeling; analysis of statistics for all SMEs of each of the regions in Russia; modeling of the weights of small, medium-sized enterprises, individual entrepreneurs in the overall indicators of SMEs and their distribution by regions of Russia is based on the functions of the density of normal distribution. Association of regions of the country with similar indicators is based on cluster analysis using the k-means method. The nine functions of the normal distribution density obtained in the course of the computational experiment have a high quality of approximation of the empirical data, which was confirmed by the Kolmogorov-Smirnov, Pierson and Shapiro-Wilk tests. Clusters have been formed that unite the regions of the country with similar indicators, namely, the specific weights of production, the number of employees and the number of business entities. The results can be used to solve the problems of institutional, financial and infrastructural support for the development of entrepreneurship in the regions of Russia, and the proposed methodology is applicable for studying the activities of territorial aggregates of enterprises of any state.