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The paper assumes a Bayesian estimate of the telecommunication systems availability ratio. Downtime and uptime are described by gamma distributions with positive integer parameters. Estimates of the distribution parameters are obtained using the maximum likelihood method. For the set samples, the values of the desired probability distribution densities are found and an expression for estimating the availability ratio is derived. Numerical estimates for the standard and assumed estimates are given. For a system with two states, a Bayesian estimate of the availability function with consideration of downtime and serviceable condition takes into account the features of backup equipment and the effect of its failure defined by performance reliability and features that ensure the reliability of information signals. The proposed Bayesian approach has the following advantages: it is possible to conduct quantitative estimates with lack of sufficient statistics on functional use indicators; it takes into account all destabilizing factors of various nature; the presence of a lower mean square error compared to traditional methods. To implement the proposed approach that estimates the availability ratio, confidence probabilities are introduced relative to the indicator of failure flows and equipment recovery. The parameters of the a priori information can be determined by different methods or on the basis of sufficient statistical data. To illustrate the discussed calculation algorithm, a digital data transmission system of a standard satellite navigation system consisting of terminal, radio equipment, and a transponder is considered. To estimate the required values, we used data on interruptions in the operation of equipment due to its malfunction during a conditional year. The frequency of downtime caused by signal propagation conditions and equipment failures was evaluated. It was shown that the gamma distribution is suitable for describing the frequency distribution of downtime. The frequency distribution of the cyclicity coefficient with the condition of the selected time interval was also taken into account. Sample mathematical expectations and mean square deviations of the downtime coefficient were found. As a result, the numerical example shows the correctness of using the Bayesian estimate of weighted equipment preparedness.

Abstract In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana–Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if R 0 < 1 $\mathcal{R}_{0}

Adoption of responsible managerial decisions in the conditions of potentially large or even "catastrophic" economic losses requires, apart from expert evaluation, the obligatory use of objective scientific approaches to the assessment of the possible risks. Such methods allow one to give an objective assessment of the risks in the current or forecasted critical situation. The article proposes a stochastic model for estimation of the productivity losses probability in the crop production in the conditions of various climatic scenarios, including the "bad" and "abnormally bad" seasons. The approach is based on the use of a modified algorithm for estimating the parameters of the finite mixture of distributions to the retrospective information about the productivity of the crop in a given geographic area within the previous years. The adequacy of the model is tested based on the real data. Extensive statistical material is accumulated at Russian agricultural research institutes for implementing the proposed approach in the various soil-climatic zones of the Russian Federation. [ABSTRACT FROM AUTHOR]

The estimation of the parameters in the population is the main problem of Statistics. Researchers take into consideration small samples for their experiments and is here where the Bootstrap Method gives a solution to the problem stated for the estimation of the parameters of the populations. The development of the automated system 1.0 satisfy the requirements of the Bootstrap Method and with the system format because it is an easy software to work with Windows to estimate parameters (¯XBOOT, s²BOOT, sBOOT, cvBOOT) in investigations of Agrarian Mechanization, showing a greater exactness in the estimations analyzed in this form. [ABSTRACT FROM AUTHOR]