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

Abstract

The accuracy of error propagation calculations is estimated for the transformation → = ( ) of the normally distributed random variable . The estimation is based on the formulas for the error propagation obtained for the inverse transformation → of the normally distributed random variable . In the general case, the calculation accuracy for the mean value and the variance of the random variable is shown to be of the first order of magnitude in the variance of the random variable . K e y w o r d s: error propagation, variance, mean value, normal distribution.

Статистичний аналіз нормально розподілених даних із обмеженим інтервалом розсіяння значень, перетворених прямими g(x) = x2; cos x; ax та оберненими до них функціями

“…Such formulas were proposed by the author [5][6][7] for elementary functions of direct 𝑔(𝑋) = 𝑋 2 ; cos 𝑋; 𝑎 𝑋 and inverse 𝑔 −1 (𝑋) = √ 𝑋; arccos 𝑋; log 𝑎 𝑋 transformations of a normally distributed RV𝑋. Despite the fact that critical remarks were made about the algorithm of substantiation of EPF [8,9], the appearance of works [5,4] indicates the need to return to the study of the relevant statistical problem, which is the subject of this work. The conclusions obtained in the work are tested by the method of one-dimensional optimization of the quadratic variance functional 𝐷 𝑋 .…”