The rate of normal approximation for the distribution of the number of multiple repetitions of characters in a stationary random sequence
We study the asymptotic normality of the number of r-fold characters repetitions in a segment of length n of a strictly stationary random sequence with values in a nite set that satis es the uniformly strong mixing condition. It is shown that if there exists a number > 0 such that the uniformly strong mixing coe cient '(t) decreases as t􀀀6􀀀 , then the distance in the uniform metric between the distribution function of the standardized number of repetitions of multiplicity r and the distribution function of the standard normal law decreases at a rate of O(n􀀀 ) for any 2 (0; (32 + 4 )􀀀1) with increasing of segment length n.