Some Features of the Direct and Inverse Transformation of Random Variables

Always actual tasks of obtaining and processing experimental results in complex systems. Random obstacles (errors), measurement errors, imperfections and limitations of mathematical models and data processing algorithms can change the appearance of the distribution and lead to incorrect use of algorithms, for example, as is the case with Kalman filtering in control systems. Complex methods for the identification of distribution laws require the study of quantum systems, natural phenomena, environmental, biological, etc. processes, which are characterized by the presence of singularities and multimodality of distributions. Therefore, it is often not recommended to apply separate distribution laws to simulate probabilistic experimental data distributions, but a generalized distribution as a single statistical system, which known distributions include as individual partial cases. Thus, the generalized gamma distribution includes Rayleigh, Maxwell, Weibull, Levy, Hi-Square distributions, which are widely used in applied problems associated with statistical methods of physical processes research, remote sensing, in the theory of reliability, for describing the dispersion composition of particles fragmentation and calculation of the efficiency of phase separation in gas-liquid streams.