Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p|X| and √ X

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dc.citation.epage325
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage318
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorКособуцький, П. С.
dc.contributor.authorКаркульовська, М. С.
dc.contributor.authorKosobutskyy, P. S.
dc.contributor.authorKarkulovska, M. S.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:14:21Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ роботі виконані теоретичні дослідження закономірностей формування статистично усереднених і дисперсії нормально розподілених випадкових значень із необмеженим інтервалом значень аргументу, які перетворені нелінійним перетворенням функціями p |X| та √ X. Показано, що для нелінійного перетворення нормально розподіленої випадкової змінної квадратним коренем, інтеграли статистичного усереднення вищих порядків n > 1 задовольняють нерівність (y − Y )n 6= 0. На основі проведених теоретичних досліджень запропоновано коректні граничні m, σ → ∞.
dc.description.abstractThis paper presents theoretical studies of formation regularities for the statistical mean and variance of normally distributed random values with the unlimited argument values subjected to nonlinear transformations of functions |X| and X. It is shown that for nonlinear square root transformation of a normally distributed random variable, the integrals of higher order mean n>1 satisfy the inequality (y−Y¯¯¯¯)n¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯≠0. On the basis of the theoretical research, the correct boundaries m,σ→∞ of error transfer formulas are suggested.
dc.format.extent318-325
dc.format.pages8
dc.identifier.citationKosobutskyy P. S. Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p|X| and √ X / P. S. Kosobutskyy, M. S. Karkulovska // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 318–325.
dc.identifier.citationenKosobutskyy P. S. Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p|X| and √ X / P. S. Kosobutskyy, M. S. Karkulovska // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 318–325.
dc.identifier.doidoi.org/10.23939/mmc2022.02.318
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63432
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 2 (9), 2022
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dc.relation.references[7] Leone F. C., Nelson L. S., Nottingham R. B. The folded normal distribution. Technometrics. 3 (4), 543–550 (1961).
dc.relation.references[8] Gui W., Chen P.-H., Wu H. A Folded Normal Slash Distribution and its Applications to Non-negative Measurements. Journal of Data Science. 11 (2), 231–247 (2013).
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dc.relation.references[11] Vattulainen I., Ala-Nissila T., Kanakaala K. Physical tests for random numbers simulations. Physical Review Letters. 73 (19), 2513–2516 (1994).
dc.relation.references[12] Lang T. Twently Statistical Errors Even You Can Find in Biomedical Research Articles. Croatian Medical Journal. 45 (4), 361–370 (2004).
dc.relation.references[13] Prudnikov A. P., Brychkov Yu. A., Marichev O. I. Integraly i rjady. Elementarnye funkcii. Moskva, Nauka (1981), (in Russian).
dc.relation.references[14] Ng E. W., Geller M. A Table o f Integrals of the Error Functions. Journal of Research of the National Bureau of Standerds – B. Mathematical Sciences. 73B (1), 1–20 (1969).
dc.relation.references[15] From Web Resource: Table of Integrals. 2014 From http://integral-table.com.
dc.relation.references[16] Kosobutskyy P. S. On the simulation of the mathematical expectation and variance of samples for gaussiandistributed random variables. Ukrainian Journal of Physics. 62 (2), 827–831 (2017).
dc.relation.references[17] Kosobutskyy P. S. Analytical relations for the mathematical expectation and variance of a standard distributed random variable subjected to the √x transformation. Ukrainian Journal of Physics. 63 (3), 215–219 (2018).
dc.relation.referencesen[1] Weisstein E. W. Cauchy Distribution. From MathWorld-A Wolfram Web Resource.
dc.relation.referencesen[2] Hudson D. Lectures on probability theory and elementary statistics. Geneva, CERN (1963).
dc.relation.referencesen[3] Suhir E. Applied Probability for Engineers and Scientistics. McGraw-Hill Companies (1997).
dc.relation.referencesen[4] Papoulis A. Probability, Random Variables, and Stochastic Processes. McGraw-Hill (1991).
dc.relation.referencesen[5] Kodolov I. M., Khudyakov S. T. Teoreticheskie osnovy verojtnostnyh metodov v inzhenernoeconomicheskich zadachah. Funkcional’nye pereobrazovanij sluchajnyh velechyn i sluchajnye fynkcii. Moskva, MADI (1985), (in Russian).
dc.relation.referencesen[6] Romanenko V. I., Kornilovska N. V. On the accuracy of error propagation calculations by analytic formulas obtained for the inverse transformation. Ukrainian Journal of Physics. 64 (3), 217–222 (2019).
dc.relation.referencesen[7] Leone F. C., Nelson L. S., Nottingham R. B. The folded normal distribution. Technometrics. 3 (4), 543–550 (1961).
dc.relation.referencesen[8] Gui W., Chen P.-H., Wu H. A Folded Normal Slash Distribution and its Applications to Non-negative Measurements. Journal of Data Science. 11 (2), 231–247 (2013).
dc.relation.referencesen[9] Rode G. G. Propagation of the Measurement Errors and Measured Means of Physical Quantities for The Elementary Functions x2 and √x. Ukrainian Journal of Physics. 62 (2), 184–191 (2017).
dc.relation.referencesen[10] Fotiadis D., Scheuring S., M¨uller S. A., Engel A., M¨uller D. J. Imaging and manipulation of biological structures with the AFM. Micron. 33 (4), 385–397 (2002).
dc.relation.referencesen[11] Vattulainen I., Ala-Nissila T., Kanakaala K. Physical tests for random numbers simulations. Physical Review Letters. 73 (19), 2513–2516 (1994).
dc.relation.referencesen[12] Lang T. Twently Statistical Errors Even You Can Find in Biomedical Research Articles. Croatian Medical Journal. 45 (4), 361–370 (2004).
dc.relation.referencesen[13] Prudnikov A. P., Brychkov Yu. A., Marichev O. I. Integraly i rjady. Elementarnye funkcii. Moskva, Nauka (1981), (in Russian).
dc.relation.referencesen[14] Ng E. W., Geller M. A Table o f Integrals of the Error Functions. Journal of Research of the National Bureau of Standerds – B. Mathematical Sciences. 73B (1), 1–20 (1969).
dc.relation.referencesen[15] From Web Resource: Table of Integrals. 2014 From http://integral-table.com.
dc.relation.referencesen[16] Kosobutskyy P. S. On the simulation of the mathematical expectation and variance of samples for gaussiandistributed random variables. Ukrainian Journal of Physics. 62 (2), 827–831 (2017).
dc.relation.referencesen[17] Kosobutskyy P. S. Analytical relations for the mathematical expectation and variance of a standard distributed random variable subjected to the √x transformation. Ukrainian Journal of Physics. 63 (3), 215–219 (2018).
dc.relation.urihttp://integral-table.com
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectстатистичні середнє
dc.subjectдисперсія
dc.subjectперетворення
dc.subjectнормальний розподіл
dc.subjectвипадкова величина
dc.subjectstatistical mean
dc.subjectvariance
dc.subjecttransformation
dc.subjectnormal distribution
dc.subjectrandom variable
dc.titleSimulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions p|X| and √ X
dc.title.alternativeМоделювання статистичних середніх і дисперсії нормально розподілених випадкових величин, перетворених нелінійними функціями p|X| та √ X
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 2