In recent years women entrepreneurs have made a significant contribution to the economic growth of most countries. Therefore, at the present stage of the entrepreneurship study, it is relevant to analyze the patterns that characterize the current level of women's entrepreneurial activity as well as determine the sectoral structure of women's entrepreneurship. The purpose of the study is a comprehensive assessment of women's early entrepreneurial activity and their sectoral preferences in creating their own business. In the course of the study, the results of the report on the global monitoring project for female entrepreneurship for the years 2016-2017 as to 74 countries is used. The levels of entrepreneurial activity of women in these countries also reviewed. The sectoral structure of women's entrepreneurship was assessed in five groups including typical types of economic activity by using normal density distribution functions. According to the results of the researches, conclusions were drawn on the predominance of such types of economic activity as trade (46.54%), health care, education and social services (19.22%), management and personal services as (15.70%). The obtained results can be used by entrepreneurs as well as by government bodies related to the business activities regulation. In the article, the original tools for assessing the sectoral structure of women's entrepreneurship is proposed.

Cessation of business has received insufficient attention in the works of domestic and foreign scientists. However, sooner or later, each entrepreneur ceases to operate.

Increasing the innovation activity of small enterprises is an urgent problem in Russia and its regions. Innovations include both the production of new or improved products (goods and services) that are significantly different from previously produced products, and the introduction of new or more advanced production processes in enterprises that are significantly different from those that were previously used. The aim of the study was to assess the levels of innovation use based on the specific weight of small innovative enterprises in the total number of small enterprises in the regions of Russia. The study used mathematical modeling of empirical data for all regions and the construction of the corresponding density functions of the normal distribution. The official information of the Federal State Statistics Service for 2015, 2017 and 2019 was considered as the initial empirical data. The study included the study of indicators that characterize the share of small innovative enterprises. The average values of the indicators were determined, as well as the ranges of their changes in the regions of Russia. The conclusions of the study, which contain scientific novelty and originality, are as follows: it is proposed to use economic and mathematical models to evaluate the values of indicators that characterize the innovation activity of small enterprises; it is shown that almost every twentieth small enterprise in Russia showed a certain innovation activity during the period under review; it is shown that the values of the specific weights of small innovative enterprises in the total number of small enterprises were significantly differentiated by region; the regions with the maximum and minimum values of the specific weights of small innovative enterprises are identified.

The study of the sectoral characteristics of early-stage entrepreneurial activity is one of the topical issues in modern research. The aim of the study is to assess the existing level of specialization of nascent entrepreneurs in modern national economies. The source of information for the analysis of the industry specialization of nascent entrepreneurs was the data provided in the Global Entrepreneurship Monitor project. The research methodology involved economics modeling with normal density function. The result of the computational experiment is the assessment of the indicator values characterizing the involvement of nascent entrepreneurs in the production and service sectors of national economies. A comparative analysis of the values of indicators for Russia and the foreign countries was carried out. It has been proved that nascent entrepreneurs in the countries under consideration are on average 4 times more likely to start activities in the service sector than in the commodity producing sector.