Recent decades have shown an increasing role of entrepreneurship in both economically developed and developing national economies. The purpose of the research is the estimation of the indicators that describe the proportion of voluntary, demanding and forced entrepreneurs in the total number of early entrepreneurs. The existing ratio of entrepreneurs with different motivation was also evaluated. The study used empirical data obtained in 2018 and presented in the Global entrepreneurship monitoring report. The normal distribution functions were used to develop economic and mathematical models for approximating initial data and evaluating four indicators of early entrepreneurs motivation in different countries.