Presented the results of evaluation of structural connection, identity and interchangeability of main asymmetric types of theoretical distributions most often acceptable for assessing the distributions of various indicators in geology and technology. The method of empirical analysis and statistical inference was used with the involvement of nonparametric facts according to the distribution patterns. The analysis of the empirical results of the application of the lognormal, gamma distribution and the Weibull distribution with the involvement of extensive statistical data from literary and research sources is carried out. The characteristic features and statistical regularities of distributions inherent to them are revealed, estimated statistical conclusions are obtained, according to which structural relationships between the functions of the lognormal, gamma and Weibull distributions are revealed. The identity and authenticity of the development of probabilistic frequencies in their application have been established, the complex geometric "image" of asymmetry inherent to these types of distributions is generalized. Structural relationships and interchangeability of asymmetric types of distributions are recommended to increase the reliability and credibility of the estimated choice of distribution in conditions of uncertainty and insignificance of statistical data when solving problems associated with forecasts, technological and computer developments.
The energy spectrum for stochastic eddies with gamma distribution