On the Rate of Convergence of Distributions of Random Variables

The rate of convergence of distributions of random variables is studied. uniform estimates for the closeness of two distribution functions of fairly general form is also obtained. For any positive numbers and any positive integer, some functions are defined. If there exists an absolute constant, and for a positive natural number there exists a positive integer, there exists a realvalued function depending on a sequence of positive numbers. A more general case where the limit distribution is assumed to be a continuous function satisfying the Lipschitz condition is also considered. For a positive integer and a sequence of positive integers, there exists a positive integer such that the distribution function of the variable satisfies a certain relation.