Information properties of symmetric and nonsymmetric models

Control over stochastic objects can be achieved by analyzing the array properties of output distributions. Since the change in the state of the complex system is characterized by changes in system behavior, and these changes are manifested in changes in the distribution of output values, it is relevant to develop methods for analyzing output data arrays to identify hidden data patterns. To achieve this goal, the paper investigates uncertainty estimates for symmetric models, previously obtained from the symmetric mapping of asymmetric realizations of subfamilies of the generalized beta distribution of the first kind. In particular, estimates of the entropies of symmetric models are obtained and used to construct the shape measure, called the entropy coefficient. When both shape measures, such as entropy coefficients and antikurtosis, are combined, it is possible to construct the space for graphical classification of symmetric distributions. The resulting space of shape measures enables both the comparative analysis of the composition of the shape implementations of the beta first kind and the Kuramaswamy subfamilies, and the classification of the output data. In particular, it is shown that the Kuramaswamy subfamily is characterized by high flexibility in modeling leptocurtic realizations with excess kurtosis exceeding 3, and it is compared with the beta subfamily of the first kind. The use of the beta subfamily of the first kind for modeling on the boundary of platycurtosis distributions is more preferable.