SPACE OF ENTROPY-PARAMETRIC CHARACTERISTICS FOR CONTROL OF THE NON-SYMMETRIC DISTRIBUTIONS FORM

• Main Author: V. G. Polosin
• Format: Article
• Language: English
• Published: Penza State University Publishing House 2020-10-01
• Series: Известия высших учебных заведений. Поволжский регион:Технические науки
• Subjects: informational and probabilistic signs; entropy coefficient; antikurtosis; asymmetry; shape of nonsymmetric distribution

Background. The task of most experimental studies is to establish an adequate distribution model based on the analysis of sample data of the observed object. Despite the good algorithmization of the choice of model parameters, the problem of choosing the shape of a mathematical model remains poorly formalized. The traditionally used graphical methods for establishing the shape of dependencies are limited by the qualitative correspondence of the model and the obtained results, since existing methods for classifying models based on only probabilistic signs do not allow us to identify differences in the shapes of close distribution families. In this regard, the actual construction of a space for classification and approximate identification of distribution shapes by a combination of information and probability signs. Materials and methods. The work contains an analysis of the shortcomings of the common method for approximate determination of the shape of nonsymmetric distributions based on the asymmetry and the kurtosis. The paper proposes to use the entropy coefficient as a feature for formalizing information signs of nonsymmetric distributions. The joint use of informational and probabilistic signs allowed us to develop a feature space for entropy – parametric analysis and control of the shape of nonsymmetric distributions. Results. The application of the mathematical formalization of the entropy – parametric signs of nonsymmetric distributions to the family of generalized gamma distributions allowed us to distinguish many distinguishable shapes of the Weibull – Gnedenko distribution families, the gamma distribution, the logarithmic normal distribution, exponential distributions, and Pearson distributions. The boundaries of the application of the Pareto distribution for constructing a model simplification are estimated. Conclusions. The paper contains material illustrating the promising use of the space of entropy-parametric signs for classification and the approximate shape of asymmetric distributions.