ESTIMATION OF THE NUMBER OF TERMS OF THE NORMAL APPROXIMATION OF THE SUMS OF INDEPENDENT RANDOM VARIABLES // BSU Bulletin. Mathematics, Informatics. - 2022. №1. . - С. 26-34.

ESTIMATION OF THE NUMBER OF TERMS OF THE NORMAL APPROXIMATION OF THE SUMS OF INDEPENDENT RANDOM VARIABLES

DOI: 10.18101/2304-5728-2022-1-26-34 UDK: 519.21

The paper solves the problem of determining the number of independent random variables with the same mathematical expectations and different variances, the sum of which has a normal distribution law with a given accuracy. A similar problem is considered for an arithmetic mean sample from a normal probability distribution. The theorem is proved and the corollary from it is obtained. The proof of the theorem is based on the decomposition of characteristic functions into a Maclaurin series. Based on the dependencies obtained in the theorem, tables are calculated to determine the required number of terms for a given accuracy for different mean square deviations of sample observations. Graphs of the obtained dependencies are constructed. The de- pendence of the required number of terms on the accuracy is approximated by a poly- nomial of the sixth degree. The theorem proved in the article and the obtained depend- encies can be used in testing, monitoring, observation and diagnostics systems.

central limit theorem, Rayleigh distribution, sample mean, variance, recurrent method, characteristic function, Maclaurin series, accuracy, relative error.