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Theoretical Backgrounds of Applied Discrete Mathematics
About the rate of normal approximation for the distribution of the number of repetitions in a stationary discrete random sequence
V. G. Mikhailova, N. M. Mezhennayab a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Bauman Moscow State Technical University, Moscow, Russia
Abstract:
The paper presents the problem of asymptotic normality of the number of r-fold repetitions of characters in a segment of a (strictly) stationary discrete random sequence on the set {1,2,…,N} with the uniformly strong mixing property. It is shown that in the case when the uniformly strong mixing coefficient φ(t) for an arbitrarily given α>0 decreases as t−6−α, then the distance in the uniform metric between the distribution function of the number of repetitions and the distribution function of the standard normal law decreases at a rate of O(n−δ) with increasing sequence length n for any δ∈(0;α(32+4α)−1)).
Keywords:
normal approximation, number of multiple repetitions, stationary random sequence, uniformly strong mixing, distance in uniform metric.
Citation:
V. G. Mikhailov, N. M. Mezhennaya, “About the rate of normal approximation for the distribution of the number of repetitions in a stationary discrete random sequence”, Prikl. Diskr. Mat., 2022, no. 58, 15–21
Linking options:
https://www.mathnet.ru/eng/pdm781 https://www.mathnet.ru/eng/pdm/y2022/i4/p15
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Abstract page: | 84 | Full-text PDF : | 18 | References: | 24 |
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