On the Accuracy of Error Propagation Calculations by Analytic Formulas Obtained for the Inverse Transformation

  • V. I. Romanenko Institute of Physics, Nat. Acad. of Sci. of Ukraine
  • N. V. Kornilovska Kherson National Technical University
Keywords: error propagation, variance, mean value, normal distribution

Abstract

The accuracy of error propagation calculations is estimated for the transformation x → y = f(x) of the normally distributed random variable x. The estimation is based on the formulas for the error propagation obtained for the inverse transformation y → x of the normally distributed random variable y. In the general case, the calculation accuracy for the mean value and the variance of the random variable y is shown to be of the first order of magnitude in the variance of the random variable x.

Author Biography

N. V. Kornilovska, Kherson National Technical University

Кафедра інформатики і комп'ютерних наук, доцент

References

D.J. Hudson. Lectures on Elementary Statistics and Probability (CERN, 1963).

G.G. Rode. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos x and arccos x. Ukr. J. Phys. 61, 345 (2016). https://doi.org/10.15407/ujpe61.04.0345

G.G. Rode. Propagation of the measurement errors and measured means of physical quantities for the elementary functions x^2 and vx. Ukr. J. Phys. 62, 184 (2017). https://doi.org/10.15407/ujpe62.02.0184

P. Kosobutsky. Analytical relations for the mathematical expectation and variance of a standard distributed random variable subjected to the vx transformation. Ukr. J. Phys. 63, 215 (2018). https://doi.org/10.15407/ujpe63.3.215

Published
2019-04-01
How to Cite
Romanenko, V., & Kornilovska, N. (2019). On the Accuracy of Error Propagation Calculations by Analytic Formulas Obtained for the Inverse Transformation. Ukrainian Journal of Physics, 64(3), 217. https://doi.org/10.15407/ujpe64.3.217
Section
General physics