THE NON-CLASSICAL ERROR THEORY OF MEASUMERMENTS (THE NETM) - AS A NEW EFFECTIVE METHOD OF MATHEMATICAL PROCESSING OF MODERN SCIENTIFIC EXPERIMENTS
 
Więcej
Ukryj
1
Academician Stepan Demianchuk International University of Economics and Humanities (IUEH), Ukraine, Rivne
AUTOR DO KORESPONDENCJI
Joseph Joseph Dzhun   

Academician Stepan Demianchuk International University of Economics and Humanities (IUEH), Ukraine, Rivne
Data nadesłania: 01-04-2019
Data akceptacji: 30-06-2020
Data publikacji: 21-07-2020
 
JoMS 2020;44(1):241–253
 
SŁOWA KLUCZOWE
DZIEDZINY
_Inne
 
STRESZCZENIE ARTYKUŁU
Objectives:
To acquaint experimental scientists with the NETM axioms, features and areas of its use, the results of checking the adequacy of its postulates at the Main Astronomical Observatory of the Academy of Sciences of Ukraine.

Material and 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.

Results:
The justified necessity of applying the new error law with the volumes of samples n > 500, in accordance with the recommendations of professor of the University of Cambridge H. Jeffreys.

Conclusions:
The Non-clasical Error Theory, which was created at the Faculty of Cybernetics of the Academician Stepan Demianchuk International University of Economics and Humanitiesr in 2015, has passed many years of testing and proved its effectiveness in the mathematical processing of modern scientific and technical measuring experiments of a large volume. The use of the NETM in the analysis 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 - the Pearson-Jeffreys law and its most important characteristic - the parameter m, which is a measure of the deviation of the statistical distribution from the Gauss law and is the main metrological characteristic of the observation method. 3). Solve the problem of weighing abnormal errors.

 
REFERENCJE (40)
1.
AES (2003). Astronomichny encyklopedychny slovnyk [Astronomical encyklopaedy diсtionary] Lviv. - 548 c.
 
2.
Dzhun, I. V. (1974). Analiz parallelnyih shirotnyih nablyudeniy, vypolnennyh po obschey programme [Analysis of parallel latitudinal observations performed under the general program]: avtoref. dis… na soiskanie uch. steneni kand. fiz.-matem. nauk: spets. 01.03.01 «Astrometriya i nebesnaya mehanika» [«Astrometry and Celestial Mechanics»]. Kyiv: Institut matematiki AN USSR,…19 p.
 
3.
Dzhun, I. V. (1984). Arnautov G. P., Stus Yu. F., Sheglov S. N. Osobennost zakona raspredeieniya rezultatov ballisticheskih izmereniy uskoreniya silyi tyazhesti [A feature of the distribution law of the results of ballistic measurements of acceleration due to the gravity]. Povtornie gravimetricheskie nablyudeniya [Repeated Gravimetric Observation]. Izd. MGK pri Prezidiume AN SSSR i NPO “Neftegeofizika”. Moscov: 1984, pp. 87-100.
 
4.
Dzhun, I. V. (1989). Ob approksimacii plotnosti verojatnosti nekotorych rjadov oshibok geodezicheskih izmerenij raspredeleniem Pirsona VІІ tіpa. [On approximating the Probability Density of Some Error Series in Geodetic Measurements by the Pearson Distribution of type VII] / Izvestija VUZ. Geodeziya i Aerofotos’emka, № 6, - pp. 43-48.
 
5.
Dzhun, I. V. (1991). Pearson’s Distribution of Type VII of Errors of satellite Laser Ranging Data. // Kinematics and Physics of Celestial Bodies, - vol. 7, pp. 74-84. Allerton Press, Inc. New York.
 
6.
Dzhun, I. V. (1992). About make use of Pearson ‘s Distribution of Type VII of the Approximation of observation’s Errors in Astrometry. // Measurements Techniques, - vol. 35. - № 3. Springer.
 
7.
Dzhun, I. V., Slavinskaja A. A. (1988). Obrabotka nablyudenij na astroljabiy Danzhona s uchetom ekscesa zakona oshibok ostatochnych pogreshnostej [Treatment of Observations on the Danjon Astrolabe given Excess Residual Error of the law of Error]. /Izuchenie Zemli kak planety metodami geofiziki, geodezii i astronomii. Tr. // Orlovskoj konferencii (Poltava, 22 sentjabrya – 3 oktjabrya 1986 g.) -K.: Naukova dumka, 1988 g, 222-226 p.
 
8.
Dzhun, I.V. (1992). Matematicheskaja obrabotka astronomicheskoj i kosmicheskoj informacii pri negaussovych osibkach nabljudenij: avtoreferat dis. na soisk. uch. stepeni doctora fiz.-mat. nauk: spec. 01.03.01 “Astrometrija i nebesnaja mechanika” Kiev, GAO NAN Ukraine, Kiev, - 46 s. [ Mathematical Treatment of Astronomical and Space-Based Information in non-Gaussian Observation Errors: Extended Abstract of Doctoral Dissertation in Physics and Mathematics, Gol. Astron. Observ. Akad. Nauk Ukrainy. Kiev, - 46 p.
 
9.
Dzhun, I.V. (1998). The Problem of Probability Methods in Economics. // Economica Firiem, 1998. Bardejovske Kupele. 5.5 – 6-5. – 1998, pp. 444-448.
 
10.
Dzhun, I.V. Novitskii, P.V. (1992). Comments of Use of the Type VII Pearson Law in Astrometry. // Kinematics and Physics of Celestial Bodies, vol. 8. № 5. pp. 78-81. Allerton Press. Inc. – New York.
 
11.
Dzhun, I.V., Gazda, V. (2002). About Distribution of Stock Index Returns Fluctuations. // Business Review. Scientific Jornal of the Faculty of Business Economics of the Univercity of Economics in Bratislava with a seat in Kosice, vol. 1, pp. 20-27.
 
12.
Dzhun, I.V., Somov, V. I. (1995). O nekotorych fundamentalnych voprosach mathematicheskoj obrabotki geofizicheskoi informacii [About some Fundamental Question of the Mathematical Treatment of the Geophysical Informations] / Ceodinamicheskie ussledovanija v Ukraine. Sb. nauch. trudov Instituta geofiziki NAN Ukrainy [Ceodinamics Investigation in Ukraine. Coll. of scientific Works Geophysical Institute NAS Ukraine, Kiev, pp. 167-178.
 
13.
Dzhun, J.V. (2010). Garold Dzheffric i jogo zakon pochibok. [Harod Jeffreys and its Errors Law] / Geodezija, kartografija i aerofotoznimannja, Ukraine, Lviv, № 73, pp. 133-137.
 
14.
Dzhun, J.V. (2011). Method for diagnostics of the mathematical models in theoretical astronomy and astrometry, “Kinematics and Physics of Celestial Bodies”, vol. 27, № 5, p. 260-264, Allerton Press, Inc.
 
15.
Dzhun, J.V. (2012). Distribution of Errors in Multiple Large Volume Observations. // Measurement Techniques. Vol. 55, № 4, p. 393-396, Springer.
 
16.
Dzhun, J.V. (2012). What are differences “observation-calculation” bound to be during modern experiments in astrometry, “Kinematics and Physics of Celestial Bodies”, vol. 28, № 1, p. 70-78, Allerton Press, Inc.
 
17.
Dzhun, J.V. (2015). Neclasichskaya teoriya peogreshnostey izmereniy [Non-classical Error Theory in Measurement] Rivne, Estero Publ., p. 168.
 
18.
Dzhun, J.V., Gazda V. (2003). O neplatnosti predpolady normality rozdelenia vynosnosti kapitalovych aktiv. // Economic Review. Quarterly Journal of the Univercity of Economics Bratislava, vol. XXXII, № 3, pp. 303-308.
 
19.
Gauss, C.F. (1823). Theoriae combinationis observationum erroribis minimis obnoxiae.
 
20.
Gazda, V. (1999). Normal Probability Distribution in Financial Theory – False Assumption and Consequences. In: Proccedings of the conference “The Process of Education and Upbringing in Higher and Learning Schools – the Ways of Development and Improvement”. Rivne: International University in Rivne, pp. 73-75.
 
21.
Gazda, V., Dzhun, J.V. (1999). About the Distribution of random Oscilations of Stock Index RMS – 100. Economika Firiem. Kosice: 9 – 10.09.1999.
 
22.
Geary, R.C. (1936). Distribution of student’s ratio for non-normal samples, “Journal of the Royal Statistical Society”, suppl. 3.
 
23.
Hattory, T. (1951). Latitude observations with floating zenith telescope at Mizusawa. PILOM, vol., № 1.
 
24.
IGC – Data (1959) on Longitude and Latitude, part. 1 / Observed at the ILS of Mizusawa, Tokyo.
 
25.
IGY – Data (1959) on Longitude and Latitude, part. 1 / Observed at the ILS of Mizusawa, Tokyo.
 
26.
Jeffreys, H. (1937). The Law of Errors and the Combinations of Observations. // Philos. Trans. Roy. Soc. London, ser. A., № 237, pp. 231-271.
 
27.
Jeffreys, H. (1939). The law of errors in the greenwich variation of latitude observations, “Mon. Not. Of the RAS”, vol. 99, № 9, р. 703-709.
 
28.
Jeffreys, H. (1940). Theory of probability, Oxford: Sec. Eddition, p. 468.
 
29.
Kemnic, Yu.V. (197). Matematicheskaja obrabotka resultatov geodezicheskich izmerenij, [Mathematical’s Treatment of the Results of geodezical’s Measurements]. Moscow: VINITI. Itogi nauki. Ser. “Geodeziya i aeros’emka”, № 7, pp. 5-23.
 
30.
Kemnic, Yu.V., Vlasov, V. D. (1978). Teorija i metodu matematicheskoj obrabotki rezultatov geodezicheskih izmerenij. [The Theory and Methods of Mathematical’s Treatment of the Results of geodezical’s Measurements] / Moscow: VINITI: Itogi nauki i techniki, ser. “Geodeziya i aeros’emka”, № 14. – 116 p.
 
31.
Khavin A. S. (1970). Yatskiv Ya. S. Izuchenie oshibok nablyudenij Goloseevckogo Kataloga zvezd shirotnych program. / [Analysis of the observational error of the Goloseyevo catalogue of latitude stars. 1.] / Astrometrija i astrofizika, № 10, pp, 34-43.
 
32.
Lukacs, E.A. (1942). A characterization of the normal distribution, Annals of Mathematical Statistics”, vol. 13, № 91.
 
33.
Malikov, M.V. (1979). Osnovy metrologii [Principles of Metrology] /Komitet po Delam Mer i izmeritelnyh Priborov pri SM SSSR, Moscow.
 
34.
Marcuze, Yu.I. (1985). Matematichescaja obrabotka resultatov geodezicheskih izmerenij. [of Mathematical’s Treatment of the Results of geodezical’s Measurements] / Moscow: VINITI: Itogi nauki i techniki, № 23, c. 3-17.
 
35.
Novickij, P.V., Zograf, P.V. (1991). Ocenka pogreshnostej rezultatov izmerenij [Estimation of Errors of the Results of the Measurements] / Energoatomizdat, Leningrad. – 304 p.
 
36.
Orlov, A.I. (1991). Chasto li racpredelenie resultatov nablydenij javliaetsja normalnym? [Is the distribution often normal?] / Zavodskaja Laboratorya, № 7, pp. 62-64.
 
37.
Pearson, K. (1902). On The mathematical theory of errors of judgment with special reference to the personal equation, “Philosophical Transactions of the Royal Society of London” Ser. A. vol.198. p. 253-296.
 
38.
Post – IGC – Data (1960) on Longitude and Latitude. Observed at the ILS of Mizusawa, Tokyo.
 
39.
Volzhanin, S.D. (1984). Metod Lp – ocenok i ego ispol’sovanie v geodezicheskih urovnitelnyh vychislenijah. [Lp – method Evoluations and its use in Geodetic Equalization Calculations] / Author’s abstract. Lvov. – 20 p.
 
40.
Yumi, S. (1962). PILOM, vol. IV, № 1.
 
eISSN:2391-789X
ISSN:1734-2031