{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T21:01:05Z","timestamp":1772139665009,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T00:00:00Z","timestamp":1673913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The article analytically summarizes the idea of applying Shannon\u2019s principle of entropy maximization to sets that represent the results of observations of the \u201cinput\u201d and \u201coutput\u201d entities of the stochastic model for evaluating variable small data. To formalize this idea, a sequential transition from the likelihood function to the likelihood functional and the Shannon entropy functional is analytically described. Shannon\u2019s entropy characterizes the uncertainty caused not only by the probabilistic nature of the parameters of the stochastic data evaluation model but also by interferences that distort the results of the measurements of the values of these parameters. Accordingly, based on the Shannon entropy, it is possible to determine the best estimates of the values of these parameters for maximally uncertain (per entropy unit) distortions that cause measurement variability. This postulate is organically transferred to the statement that the estimates of the density of the probability distribution of the parameters of the stochastic model of small data obtained as a result of Shannon entropy maximization will also take into account the fact of the variability of the process of their measurements. In the article, this principle is developed into the information technology of the parametric and non-parametric evaluation on the basis of Shannon entropy of small data measured under the influence of interferences. The article analytically formalizes three key elements: -instances of the class of parameterized stochastic models for evaluating variable small data; -methods of estimating the probability density function of their parameters, represented by normalized or interval probabilities; -approaches to generating an ensemble of random vectors of initial parameters.<\/jats:p>","DOI":"10.3390\/e25020184","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T05:36:55Z","timestamp":1673933815000},"page":"184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7607-1943","authenticated-orcid":false,"given":"Oleh","family":"Bisikalo","sequence":"first","affiliation":[{"name":"Department of Automation and Intelligent Information Technologies, Faculty of Intelligent Information Technologies and Automation, Vinnytsia National Technical University, Khmelnitske Shose Str. 95, 21000 Vinnytsia, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5352-077X","authenticated-orcid":false,"given":"Vyacheslav","family":"Kharchenko","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Networks and Cybersecurity, Faculty of Radio Electronics, Computer Systems and Information Communications, National Aerospace University KhAI, Chkalov Str. 17, 610700 Kharkiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7624-7072","authenticated-orcid":false,"given":"Viacheslav","family":"Kovtun","sequence":"additional","affiliation":[{"name":"Department of Computer Control Systems, Faculty of Intelligent Information Technologies and Automation, Vinnytsia National Technical University, Khmelnitske Shose Str. 95, 21000 Vinnytsia, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8043-0785","authenticated-orcid":false,"given":"Iurii","family":"Krak","sequence":"additional","affiliation":[{"name":"Department of Theoretical Cybernetics, Faculty of Computer Sciences and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 60, 01033 Kyiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0051-5560","authenticated-orcid":false,"given":"Sergii","family":"Pavlov","sequence":"additional","affiliation":[{"name":"Laboratory of Biomedical Optics, Department of Biomedical Engineering, Faculty for Infocommunications, Radioelectronics and Nanosystems, Vinnytsia National Technical University, Khmelnitske Shose Str. 95, 21000 Vinnytsia, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113835","DOI":"10.1016\/j.eswa.2020.113835","article-title":"A novel method for solving data envelopment analysis problems with weak ordinal data using robust measures","volume":"164","author":"Ebrahimi","year":"2021","journal-title":"Expert Syst. 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