НЕКЛАСИЧНА ТЕОРІЯ ПОХИБОК ВИМІРІВ (НТПВ) – ЯК НОВИЙ ЕФЕКТИВНИЙ ЗАСІБ МАТЕМАТИЧНОЇ ОБРОБКИ СУЧАСНИХ НАУКОВИХ ЕКСПЕРИМЕНТІВ
The non-classical error theory of measurements (the netm)– as a new effective method of mathematical processing of modern scientific experiments

Summary/Abstract: The classical error theory (CET) and the least square method (LSM) that flowfrom it, which remain one of the main tools of mathematical modeling, was createdin 1823 by the prominent German mathematician, C. F. Gauss. The CET has become widely used in mathematical processing of the results of scientific and technicalmeasurements for the last 150 years. But their number has increased immeasurablywith the beginning of the space era and the automation of measurements. However,there was their very interesting feature – discrepancy of the fundamental concept ofthe CET, which is mainly non-Gaussian character of multiple measurements, whichhave a volume n > 500. The NETM in the first approximation is based on the CETmethods but has a completely different axiomatic basis and is used for mathematicalprocessing of modern, automated scientific and technical experiments with a largevolume of measurements.\The purpose of the research: to acquaint experimental scientists with the NETMaxioms, features and areas of its use, the results of checking the adequacy of itspostulates at the Main Astronomical Observatory of the Academy of Sciences ofUkraine.Methods: probability and mathematical-statistical procedures are used in the NETM,which ensure the effectiveness of estimations of the studied parameters and diagnostics of mathematical modeling.The results of the research: the justified necessity of applying the new error law withthe volumes of samples n > 500, in accordance with the recommendations ofprofessor of the University of Cambridge H. Jeffreys.Scientific novelty: a general description of the NETM procedures is given for thefirst time for the purpose of obtaining effective evaluations of the desired parameters of statistical distributions based on the use of the Pearson-Jeffreys error lawwith observation volumes n > 500.Practical significance: the study is to uncover the universal nature of the NETMmethods in processing multiple observations of large volumes in various fields ofscience and technology.Conclusion: the Non-clasical Error Theory, which was created at the Faculty ofCybernetics of the Academician Stepan Demianchuk International Universityof Economics and Humanitiesr in 2015, has passed many years of testing andproved its effectiveness in the mathematical processing of modern scientific andtechnical measuring experiments of a large volume. The use of the NETM in theanalysis of data allows solving three important problems, namely:1) Use modern, adequate representation of the error distribution law of observations of large volumes.2) Obtain effective estimates of the fundamental distribution of the NETM – thePearson-Jeffreys law and its most important characteristic – the parameter m,which is a measure of the deviation of the statistical distribution from the Gausslaw and is the main metrological characteristic of the observation method.3) Solve the problem of weighing abnormal errors.

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