Statistical testing of uniformity of discrete probability distribution based on the Tsallis entropy

The article discusses the problems of constructing statistical criteria for testing the $s$-dimensional uniformity of a binary random sequence based on the Tsallis entropy for two types of the null hypothesis: simple and complex. In the asymptotics of the growing cardinality of the power of the alphabet, asymptotically unbiased statistical estimates of the Tsallis entropy are constructed in the cases of simple and complex null hypotheses. Based on the constructed estimates and their asymptotic distributions, statistical criteria for $s$-dimensional uniformity with a given asymptotic size are constructed. The results of computer experiments are presented.