Random and pseudo-random number generators (RNGs) were initially used to solve numerical integration problems (the Monte Carlo method). Currently, the RNGs are used in cryptography and simulation modeling. The latter one typically uses RNGs based on computer algorithms and programs. This article presents a method aimed at testing the independence of random numbers sequences (RNSs). The method is based on the sums properties of independent random variables. Algorithms based on this method operate fast. Here not only the instant statistics including correlation coefficients are analyzed, but also the properties of empirical functions of RNSs distributed sums. In this article, the analysis is limited only to the case of uniformly distributed RNSs. The calculations performed prove the high selective efficiency of the proposed criteria, which allows to reliably distinguish between dependent and independent RNSs. Due to the high operation speed, the proposed algorithms and criteria can be used for testing very long RNSs (especially in Big Data tasks).
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