Exponential estimates of sums of multidimensional random variables

This article discusses methods for estimating exponential estimates of sums of multivariate random variables. Exponential estimates are one of the topical issues in statistics and probability theory, allowing one to estimate high probabilities of random events. The article analyzes the theoretical aspects of Chernoff and Hoeffding estimates, their use and practical examples. In addition, by using the Kullback-Leibler divergence, the accuracy of estimates is increased. This article emphasizes the importance of using exponential estimates in practical and scientific research and examines their application in various fields. K