Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions
A 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 ra...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2018-06-01
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| Series: | Қарағанды университетінің хабаршысы. Физика сериясы |
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| Online Access: | https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/236 |
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| author | S.V. Zabolotnii V.Yu. Kucheruk Z.L. Warsza А.K. Khassenov |
| author_facet | S.V. Zabolotnii V.Yu. Kucheruk Z.L. Warsza А.K. Khassenov |
| author_sort | S.V. Zabolotnii |
| collection | DOAJ |
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A 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.
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| format | Article |
| id | doaj-art-71c80bdd7bf24abcaac1360b9ca51456 |
| institution | DOAJ |
| issn | 2518-7198 2663-5089 |
| language | English |
| publishDate | 2018-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Физика сериясы |
| spelling | doaj-art-71c80bdd7bf24abcaac1360b9ca514562025-08-20T03:18:06ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Физика сериясы2518-71982663-50892018-06-01902Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributionsS.V. ZabolotniiV.Yu. KucherukZ.L. WarszaА.K. Khassenov A 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. https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/236bimodal distributionmeasured parametervariance of estimatesmomentscumulantsstochastic polynomial |
| spellingShingle | S.V. Zabolotnii V.Yu. Kucheruk Z.L. Warsza А.K. Khassenov Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions Қарағанды университетінің хабаршысы. Физика сериясы bimodal distribution measured parameter variance of estimates moments cumulants stochastic polynomial |
| title | Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| title_full | Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| title_fullStr | Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| title_full_unstemmed | Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| title_short | Polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| title_sort | polynomial estimates of measurand parameters for data from bimodal mixtures of exponential distributions |
| topic | bimodal distribution measured parameter variance of estimates moments cumulants stochastic polynomial |
| url | https://phs.buketov.edu.kz/index.php/physics-vestnik/article/view/236 |
| work_keys_str_mv | AT svzabolotnii polynomialestimatesofmeasurandparametersfordatafrombimodalmixturesofexponentialdistributions AT vyukucheruk polynomialestimatesofmeasurandparametersfordatafrombimodalmixturesofexponentialdistributions AT zlwarsza polynomialestimatesofmeasurandparametersfordatafrombimodalmixturesofexponentialdistributions AT akkhassenov polynomialestimatesofmeasurandparametersfordatafrombimodalmixturesofexponentialdistributions |