THE STUDY OF DEVIATIONS FROM THE NORMAL DISTRIBUTION OF SUMS OF INDEPENDENT OR DEPENDENT RANDOM VARIABLES USING GENERAL ESTIMATES OF DIFFERENCE PSEUDO MOMENTS

Аннотация

In this article, using the method of semi invariants under the Statulevicius condition, general uneven estimates of approximation by a normal distribution are obtained and estimates of absolute pseudo moments are obtained on the basis of this. In order to obtain similar estimates in limit theorems for sums of independent or dependent random variables, it is sufficient to obtain an estimate of semi invariants of the Statulevicius type. These results can be used in tasks related to the analysis of rare events and in statistical testing tasks, where we want to test, for example, the hypothesis that the data is distributed normally. Keywords: Cumulants, the Statulevicius condition,uneven estimate, difference pseudo-moment, probabilities of large deviations.