| Summary: | 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.
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