Polynomial Estimates of Measurand Parameters for Data from Bimodal Mixtures of Exponential Distributions

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dc.contributor.authorZabolotnii, Serhii
dc.contributor.authorЗаболотній, Сергій Васильович
dc.contributor.authorKucheruk, V. Yu.
dc.contributor.authorWarsza, Zygmunt Lech
dc.contributor.authorKhassenov, А. K.
dc.date.accessioned2025-12-03T08:21:23Z
dc.date.available2025-12-03T08:21:23Z
dc.date.issued2018
dc.description.abstractA non-conventional approach to finding estimates of the result of multiple measurements for a random error model in the form of bimodal mixtures of exponential distributions is proposed. This approach is based on the application of the Polynomial Maximization Method (PMM) with the description of random variables by higher order statistics (moment & cumulant). The analytical expressions for finding estimates and analysis accuracy to the degree of the polynomial r = 3 are presented. In case when the degree of the polynomial r = 1 and r = 2 (for symmetrically distributed data) polynomial estimate equivalent can be estimated as a mean (average arithmetic). In case when the degree of the polynomial r = 3, the uncertainty of the polynomial estimate decreases. The reduction coefficient depends on the values of the 4th and 6th order cumulant coefficients that characterize the degree of difference while the distribution of sample data from the Gaussian model. By means of multiple statistical tests (Monte Carlo method), the properties of the normalization of polynomial estimates are investigated and a comparative analysis of their accuracy with known estimates (mean, median and center of folds) is made. Areas that depend on the depth of antimodality and sample size, in which polynomial estimates (for r = 3) are the most effective.
dc.identifier.citationZabolotnii S. V., Kucheruk V. Yu., Warsza Z. L., Khassenov, А. K. Polynomial Estimates of Measurand Parameters for Data from Bimodal Mixtures of Exponential Distributions. Bulletin of the Karaganda University. Physics Series. 2018. № 2 (90), рp. 71-80. [Web of Science]
dc.identifier.urihttps://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/236
dc.identifier.urihttps://dr.csbc.edu.ua/handle/123456789/695
dc.publisherKaragandy University of the name of academician E.A. Buketov
dc.subjectNATURAL SCIENCES::Physics
dc.titlePolynomial Estimates of Measurand Parameters for Data from Bimodal Mixtures of Exponential Distributions
dc.typeArticle
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