ASYMPTOTIC PROPERTIES OF AN UNKNOWN DISTRIBUTION FUNCTION AND THEOREMS RELATED TO IT

This article analyzes the asymptotic properties of unknown distribution functions and their theoretical foundations. The problems of estimating an unknown distribution function using the empirical distribution function, the main limit theorems such as the Glivenko-Cantelli theorem, the Kolmogorov-Smirnov statistic, and Donsker's theorem, as well as their practical applications are considered. The article systematically presents fundamental results in the field of modern probability theory and mathematical statistics based on literature analysis.