One of the urgent tasks in many modern scientific studies is the comparative analysis of indicators that characterize large sets of similar objects located in different regions. Given the significant differences between the regions compared, this analysis should be carried out using relative indicators. The objective of the study was to use the density functions of the normal distribution to model empirical data that describe the compared sets of objects located in different regions. The methodological approach was based on the Chebyshev and Lyapunov theorems. The research results focus on the main stages of the construction of normal distribution functions and the corresponding histograms, as well as the determination of the parameters of these functions. The work possesses a degree of originality, since it provides answers to questions such as the justification of the necessary information base; performing computational experiments and developing alternative options for the generation of normal distribution density functions; comprehensive evaluation of the quality of the functions obtained through three statistical tests: Pearson, Kolmogorov-Smirnov, Shapiro-Wilk; identification of patterns that characterize the distribution of indicators of the sets of objects considered. Examples of empirical data models are given using distribution functions to estimate the share of innovative firms in the total number of firms in the regions of Russia.

Эффективность производства в сфере сельского хозяйства непосредственно влияет на социально-экономическое развитие страны и регионов, а также на их продовольственную безопасность. Среди множества факторов устойчивого развития аграрного производства особое место, в последнее время, отводится сельскохозяйственной кооперации. Она позволяет добиться финансовой устойчивости предприятия, увеличить производительность труда в нем, снизить издержки производства, способствует развитию сельских поселений и занятости в них. Поэтому исследования в области сельскохозяйственной кооперации актуальны. Цель проведенного исследования состоит в изучении опыта поддержки сельскохозяйственных кооперативов в субъектах Российской Федерации и построении модели развития сельскохозяйственной кооперации. Были использованы различные методы исследования процессов и явлений в области организационных и экономических отношений: анализ и синтез, системный и логический подходы к изучению тенденций развития сельскохозяйственной кооперации, табличная и графическая интерпретация теоретической информации и эмпирических данных. В работе рассмотрены основные виды поддержки сельскохозяйственных кооперативов, действующих на территории нашей страны. Выявлены самые распространенные из них и проведен анализ их внедрения в различных субъектах страны по всем федеральным округам. На основании данных Единого реестра субъектов малого и среднего предпринимательства о количестве созданных в 2018 году в стране сельскохозяйственных кооперативов были выявлены лидирующие в этом вопросе регионы. Рассмотрен опыт развития сельскохозяйственной кооперации в самом успешном в этом вопросе регионе-Липецкой области. Результатом исследования является разработанная авторами модель развития сельскохозяйственной кооперации на региональном уровне. Данная модель включает в себя комплексную систему развития сельскохозяйственной кооперации, состоящую из двух элементов, (трехуровневая система управления и институты развития сельскохозяйственной кооперации) и модель поддержки развития сельскохозяйственной кооперации, что будет способствовать эффективному развитию кооперативов. Результаты исследования могут быть использованы для дальнейшего совершенствования практики поддержки сельскохозяйственной кооперации на уровне регионов.

The efficiency of production in the agriculture domain directly affects the socio-economic development of the country, the rural areas. Recently, agricultural cooperation has been held high regard among all the factors of sustainable development of the agricultural production. That allows achieving financial stability of an agricultural enterprise, increasing the labor productivity in it, and reducing production costs. On the other hand, it promotes the development of rural settlements and employment there; therefore, conducting research in the agricultural cooperation field is so relevant. The purpose of the research is to study the development of agricultural cooperation in Russia and identify the problems that hinder the cooperative movement development; and suggest the main directions for further development in the field of cooperation over the country. A variety of methods have been used to study the processes and phenomena in the field of organizational and economic relations, such as analysis and synthesis, reliance on systemic and logical approaches to study the trends in the development of agricultural cooperation, besides using the graphic interpretation of theoretical information and the empirical data. This work takes into consideration the granting support for cooperatives. In addition, it defines the main problems and conditions of the cooperatives’ effective performance and suggests directions for further development of cooperation.

The main task of production management in agricultural enterprises is to build management systems that ensure that the necessary actions and procedures are performed to obtain a market result from the operation of the enterprise’s operating system. The problem of managing crop production is quite relevant today, since most agricultural enterprises, switching exclusively to the production of crop production only, do not comply with the recommended technologies for growing crops, violate the sciencebased foundations of farming, which is associated with the lack of modern material technical base, and the difficult financial and economic situation of most farmsteads and especially insufficient level of managerial work in the field of crop production. Thus, the aim of the study is to develop recommendations for improving the organization and management of crop production in modern business conditions. As a result of the study, an analysis of the effectiveness of the organization and management of crop production at the current stage of development of the Russian economy was conducted; problems were studied, prospects for the development of the crop industry were outlined, recommendations were proposed for improving the agricultural management system, taking into account current economic conditions.

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.