UNIV. NEWS. NORTH-CAUCAS. REG. TECHNICAL SCIENCES SERIES. 2022; 3: 20-32
http://dx.doi.org/10.17213/1560-3644-2022-3-20-32
STATISTICAL IDENTIFICATION OF UNIMODAL RANDOM VARIABLES USING PARAMETRICALLY SIMILAR CONDITIONAL DISTRIBUTIONS
Lobova Tatyana V. – Senior Lecturer, Department «Applied Mathematics», npi_pm@mail.ru
Tkachev Alexander N. – Doctor of Technical Sciences, Professor, Head of the Department «Applied Mathematics», npi_pm@mail.ru
Abstract
The problem of statistical estimation of the law of distribution of a random variable by the available sample set of its values is considered. For evaluation, it is proposed to use specially selected parametrically similar basic conditional distributions. Parametric similarity is achieved by specifying the distribution parameters in such a way that the mathematical expectation, variance and mode coincide, the values of which are estimated statistically from the sample. Equations are obtained for finding the parameters of the considered distributions. A procedure is proposed for finding coefficients that have the meaning of probabilities in the additive convolution of distributions, as a result of which, on average, a minimum discrepancy between the empirical and theoretical distributions is achieved. Methods for estimating the priorities of the considered conditional distributions are described, which provide an increase in the accuracy of pointwise agreement between the theoretical and empirical distributions. The developed approach to estimating the distribution law is illustrated with examples confirming the possibility of its application for a wide range of problems in applied statistics.
Keywords: statistical identification, random variable, statistical series, conditional distributions, criterion relation, distribution priorities
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