Simulation of statistical mean and variance of normally distributed data NX(mX, σX) transformed by nonlinear functions g(X) = cos X, eX and their inverse functions g−1(X) = arccos X, ln X
| dc.citation.epage | 1022 | |
| dc.citation.issue | 4 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 1014 | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.author | Кособуцький, П. С. | |
| dc.contributor.author | Каркульовська, М. С. | |
| dc.contributor.author | Kosoboutskyy, P. S. | |
| dc.contributor.author | Karkulovska, M. S. | |
| dc.coverage.placename | Львів | |
| dc.date.accessioned | 2025-03-10T09:21:57Z | |
| dc.date.created | 2023-02-28 | |
| dc.date.issued | 2023-02-28 | |
| dc.description.abstract | Обгрунтовані аналітичні співвідношення обчислення статистичних середніх і дисперсії функцій g(X) = cos X, eX, g−1(X) = arccos X, ln X перетворення нормально NX(mX, σX) розподіленої випадкової величини. | |
| dc.description.abstract | This paper presents analytical relationships for calculating statistical mean and variances of functions g(X)=cosX, eX, g−1(X)=arccosX, lnX of transformation of a normally NX(mX, σX) distributed random variable. | |
| dc.format.extent | 1014-1022 | |
| dc.format.pages | 9 | |
| dc.identifier.citation | Kosoboutskyy P. S. Simulation of statistical mean and variance of normally distributed data NX(mX, σX) transformed by nonlinear functions g(X) = cos X, eX and their inverse functions g−1(X) = arccos X, ln X / P. S. Kosoboutskyy, M. S. Karkulovska // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1014–1022. | |
| dc.identifier.citationen | Kosoboutskyy P. S. Simulation of statistical mean and variance of normally distributed data NX(mX, σX) transformed by nonlinear functions g(X) = cos X, eX and their inverse functions g−1(X) = arccos X, ln X / P. S. Kosoboutskyy, M. S. Karkulovska // Mathematical Modeling and Computing. — Lviv Politechnic Publishing House, 2023. — Vol 10. — No 4. — P. 1014–1022. | |
| dc.identifier.doi | doi.org/10.23939/mmc2023.04.1014 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/64072 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 4 (10), 2023 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 4 (10), 2023 | |
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| dc.relation.references | [8] Bohm G., Zech G. Introduction to Statistics and data Analysis for Physics. Verlag Deutsches ElektronenSynchrotron (2010). | |
| dc.relation.references | [9] Samorodnitsky G., Taqqu M. S. Stable Non-Gaussian Random Processes. New York, Chapman and Hall (1994). | |
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| dc.relation.references | [12] Goodman J. W. Statistical Optics. John Wiley and Sons. Inc. (2015). | |
| dc.relation.references | [13] Patel J. K., Read C. B. Handbook of the Normal Distribution. New York, Dekker (1982). | |
| dc.relation.references | [14] Marvin R., Arnljot H. System Reliability Theory: Models, Statistical Methods, and Applications. John Wiley and Sons. Inc. (2004). | |
| dc.relation.references | [15] Liang T., Jia X. Z. An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices. Journal of Semiconductors. 33 (12), 125008 (2012). | |
| dc.relation.references | [16] Gu K., Jia X., You T., Liang T. The yield estimation of semiconductor products based on truncated samples. International Journal of Metrology and Quality Engineering. 4 (3), 215–220 (2013). | |
| dc.relation.references | [17] Einstein A. On the motion of particles suspended in a fluid at rest, required by the molecular-kinetic theory of heat. Collection of articles: Leningrad, ONTI-GROTL (1936). | |
| dc.relation.references | [18] Einstein A., Smolukhovsky M. Brownian motion. Collection of articles. Leningrad, ONTI-GROTL (1936). | |
| dc.relation.references | [19] Risken H. The Fokker–Planck quation. Berlin–Heidelberg, Springer (1989). | |
| dc.relation.references | [20] Gihman I., Skorochodov A. The Theory of Statistic Processes I. Springer, Berlin (2004). | |
| dc.relation.references | [21] Kosobutskyy P. S., Karkulovska M. S. Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p |X| and √ X. Mathematical Modeling and Computing. 9 (2), 318–325 (2022). | |
| dc.relation.references | [22] Rode G. G. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos X and arccos X. Ukrainian Journal of Physics. 61 (4), 345–352 (2016). | |
| dc.relation.references | [23] Dwight H. Tables of Integrals and other Mathematical data. New York, The Macmillan Company (1961). | |
| dc.relation.references | [24] Abramowitz M., Stegun I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York, Dover (1972) | |
| dc.relation.referencesen | [1] Hudson D. J. Lectures on elementary statistics and probability. Geneva, CERN (1963). | |
| dc.relation.referencesen | [2] Ku H. H. Notes on the Use of Propagation of Error Formulas. Journal of Research of the National Bureau of Standards. Section C: Engineering and Instrumentation. 70C (4), 263–273 (1966). | |
| dc.relation.referencesen | [3] Bevington P., Robinson D. K. Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, Boston (2002). | |
| dc.relation.referencesen | [4] Taylor J. R. An Introduction to Error Analysis. Univ. Sci. Books, Sausalito, CA (1997). | |
| dc.relation.referencesen | [5] Wikipedia. Propagation of uncertainty. https://en.wikipedia.org/wiki/Propagation of uncertainty. | |
| dc.relation.referencesen | [6] Suhir E. Applied Probability for Engineers and Scientistics. McGraw-Hill Companies (1997). | |
| dc.relation.referencesen | [7] Papoulis A. Probability, Random Variables, and Stochastic Processes. McGraw-Hill (1991). | |
| dc.relation.referencesen | [8] Bohm G., Zech G. Introduction to Statistics and data Analysis for Physics. Verlag Deutsches ElektronenSynchrotron (2010). | |
| dc.relation.referencesen | [9] Samorodnitsky G., Taqqu M. S. Stable Non-Gaussian Random Processes. New York, Chapman and Hall (1994). | |
| dc.relation.referencesen | [10] Wichmann E. Quantum Physics. Berkeley Physics Course. Vol. 4. McGraw-Hill Book Company (1971). | |
| dc.relation.referencesen | [11] Leach A. Molecular Modelling: Principles and Applications. Prentice Hall (2001). | |
| dc.relation.referencesen | [12] Goodman J. W. Statistical Optics. John Wiley and Sons. Inc. (2015). | |
| dc.relation.referencesen | [13] Patel J. K., Read C. B. Handbook of the Normal Distribution. New York, Dekker (1982). | |
| dc.relation.referencesen | [14] Marvin R., Arnljot H. System Reliability Theory: Models, Statistical Methods, and Applications. John Wiley and Sons. Inc. (2004). | |
| dc.relation.referencesen | [15] Liang T., Jia X. Z. An empirical formula for yield estimation from singly truncated performance data of qualified semiconductor devices. Journal of Semiconductors. 33 (12), 125008 (2012). | |
| dc.relation.referencesen | [16] Gu K., Jia X., You T., Liang T. The yield estimation of semiconductor products based on truncated samples. International Journal of Metrology and Quality Engineering. 4 (3), 215–220 (2013). | |
| dc.relation.referencesen | [17] Einstein A. On the motion of particles suspended in a fluid at rest, required by the molecular-kinetic theory of heat. Collection of articles: Leningrad, ONTI-GROTL (1936). | |
| dc.relation.referencesen | [18] Einstein A., Smolukhovsky M. Brownian motion. Collection of articles. Leningrad, ONTI-GROTL (1936). | |
| dc.relation.referencesen | [19] Risken H. The Fokker–Planck quation. Berlin–Heidelberg, Springer (1989). | |
| dc.relation.referencesen | [20] Gihman I., Skorochodov A. The Theory of Statistic Processes I. Springer, Berlin (2004). | |
| dc.relation.referencesen | [21] Kosobutskyy P. S., Karkulovska M. S. Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p |X| and √ X. Mathematical Modeling and Computing. 9 (2), 318–325 (2022). | |
| dc.relation.referencesen | [22] Rode G. G. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos X and arccos X. Ukrainian Journal of Physics. 61 (4), 345–352 (2016). | |
| dc.relation.referencesen | [23] Dwight H. Tables of Integrals and other Mathematical data. New York, The Macmillan Company (1961). | |
| dc.relation.referencesen | [24] Abramowitz M., Stegun I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York, Dover (1972) | |
| dc.relation.uri | https://en.wikipedia.org/wiki/Propagation | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2023 | |
| dc.subject | статистичне середнє | |
| dc.subject | дисперсія | |
| dc.subject | перетворення | |
| dc.subject | нормальний розподіл | |
| dc.subject | випадкова величина | |
| dc.subject | statistical mean | |
| dc.subject | variance | |
| dc.subject | transformation | |
| dc.subject | normal distribution | |
| dc.subject | random variable | |
| dc.title | Simulation of statistical mean and variance of normally distributed data NX(mX, σX) transformed by nonlinear functions g(X) = cos X, eX and their inverse functions g−1(X) = arccos X, ln X | |
| dc.title.alternative | Моделювання статистичних середнього та дисперсії нормально NX(mX, σX) розподілених даних, перетворених нелінійними функціями g(X) = cos X, eX та оберненими до них g−1(X) = arccos X, ln X | |
| dc.type | Article |
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