The book is devoted to one of the problems of mathematical statistics - distribution functions found in engineering practice. First, elementary information on probability theory is given, and then continuous and discrete distributions are considered and their applicability in solving various engineering problems. Two chapters are devoted to empirical distributions. A separate chapter is devoted to the analysis of complex systems. At the end of the monograph, a systematic bibliography is given on various sections of mathematical statistics and related disciplines. The book is intended for a wide range of specialists interested in statistical research methods.