The statistical possibilities of studying intrasystem processes in multielement systems are determined by solving the problem of the moments of distributions specified in mathematical and physical formulations. The characteristic properties of the distributions can be revealed by analyzing the simple and product moments (integer, fractional, and functional) and the relationships between them. The proposed method of complex analysis of experimental data and theoretical calculations is illustrated using the examples of the Maxwellian velocity distribution of molecules, the Planck radiation spectral power distribution, and the size distribution of microscopic particles in a disperse-hardened alloy.