Simulation of statistical mean and variance of normally distributed data $N_X(m_X,\sigma_X)$ transformed by nonlinear functions $g(X)=\cos X$, $e^X$ and their inverse functions $g^{-1}(X)=\arccos X$, $\ln X$
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Published:2023
Issue:4
Volume:10
Page:1014-1022
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ISSN:2312-9794
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Container-title:Mathematical Modeling and Computing
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language:
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Short-container-title:Math. Model. Comput.
Author:
Kosoboutskyy P. S., ,Karkulovska M. S.,
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.
Publisher
Lviv Polytechnic National University
Subject
Computational Theory and Mathematics,Computational Mathematics
Reference24 articles.
1. Hudson D. J. Lectures on elementary statistics and probability. Geneva, CERN (1963).
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).
3. Bevington P., Robinson D. K. Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, Boston (2002).
4. Taylor J. R. An Introduction to Error Analysis. Univ. Sci. Books, Sausalito, CA (1997).
5. Wikipedia. Propagation of uncertainty. https://en.wikipedia.org/wiki/Propagation of uncertainty.