Modeling the performance of small and medium entrepreneurship in regions by using density function of normal distribution

The article considers the hypothesis of feasibility of using density functions of normal distribution to stimulate the distribution of values of the indicators characterizing the aggregate of subjects of small and middle entrepreneurship. It proposes methodological approaches and main stages of formation of the information base, approximation of empirical data and construction of associated histograms. It discloses methods and tools to estimate indicators of the above functions and requirements to the source data. The paper presents estimations of the parameters of density function of normal distribution that describe such indicators, as average number of employees, turnover per company or entrepreneur and turnover per employee of small and medium enterprises, individual entrepreneurs on the basis of official statistical data by RF regions for 2013. It substantiates the conduct of complex assessment of function quality by means of goodness-of-fit indicators suggested by Pearson, Kolmogorov-Smirnov, Shapiro-Wilk. There are examples of estimating the parameters of several functions that confirm the hypothesis made in during the research. The author proposes recommendations on the analysis of obtained functions to establish patterns of activities of small and medium enterprises, individual entrepreneurs in the regions of the country, as well as the differentiation of their performance. The article recommends to consider 3 intervals of the change in the values of parameters corresponding to the half, the majority and absolute majority of Russian regions. The article presents proposals on the use of density function of normal distribution to monitor entrepreneurship development and the justification of state regulation and support of these activities.