V.M. Artyushenko1, V.I. Volovach2

1 Technological University named after twice Hero of the Soviet Union, Cosmonaut A.A. Leonov – Branch of the FSBEI HE «Moscow State University of Geodesy and Cartography» (Moscow, Russia)
2 Volga Region State University of Service (Toglyatti, Russia)
2 MIREA – Russian Technological University (Moscow, Russia)
1 artuschenko@mail.ru, 2 volovach.vi@mail.ru

The paper discusses the problem of estimating the mathematical expectation and variance of a random variable that models the uncertainty of the measurement result of a discrete indicator. The proposed approach is focused on situations where the density of the probability distribution is only partially known or specified inaccurately, which is characteristic of a number of practical problems related to the limitation or fragmentation of the source data. The article proposes a model that allows you to correctly take into account both the incompleteness of information and possible variations in the distribution structure, which ensures more reliable obtaining of statistical characteristics.

The purpose of the work is to develop and analyze a model for measuring a discrete indicator, which makes it possible to obtain posterior estimates of the mathematical expectation and variance of the latter, combining non-numerical, inaccurate and non-prior information along with statistical (empirical) information.

A posteriori estimates of the expectation and variance of the discrete indicator are obtained, which combine empirical information and non-numerical, inaccurate and incomplete information. It is shown that the proposed model of discrete parameter estimation is characterized by sufficient resistance to change of initial assumptions and good adaptability to conditions of numerical information deficit. It has been shown that the developed methodology for finding posterior estimates can be effectively applied in analyzing the reliability and predicting the states of multivariable technical systems.

The presented results are of practical importance for various branches of modern production, where it is required to form reasonable estimates of parameters in conditions of uncertainty and increased variability of measurement data.

Artyushenko V.M., Volovach V.I. The evaluation of a discrete indicator using inaccurate and incomplete information on probability distribution. Nonlinear World. 2026. V. 24. № 2. P. 5–13. DOI: https:// doi.org/10.18127/ j20700970-202602-01 (In Russian)

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