TY - JOUR
AU - Kosobutskyy, P.
PY - 2022/08/29
Y2 - 2022/10/01
TI - Statistical Analysis of Normally Distributed Data with a Limited Scattering Interval of Values Converted by Direct g(x) = x2; cos x; ax and Inverse Functions
JF - Ukrainian Journal of Physics
JA - Ukr. J. Phys.
VL - 67
IS - 5
SE - General physics
DO - 10.15407/ujpe67.5.346
UR - https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2019605
SP - 346
AB - <p>The work is devoted to the theoretical analysis of the correct application of the model of a continuous normally distributed random variable in the substantiation of the so-called error transfer formulas in the problem of a statistical processing of experimental data. Attention is paid to the role of limiting the scattering interval of values of a random variable subjected to nonlinear direct g(X) transformation by elementary functions X<sup>2</sup>; a<sup>X</sup> and cos X, as well as the inverse g<sup>-1</sup>(X) = √X, arccos X, log<sub>a</sub> X to them. The regularities of the statistical averaging of the data obtained by the disorder of the Taylor transform functions are studied. To confirm the validity of the obtained results, the method of quadratic functional optimization is used.</p>
ER -