Lithuanian Mathematical Journal

, Volume 58, Issue 2, pp 219–234 | Cite as

On the rate of convergence in the central limit theorem for random sums of strongly mixing random variables

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Abstract

We present upper bounds for supx ∈ ℝ|P{Z N  < x} − Φ(x)|, where Φ(x) is the standard normal distribution function, for random sums \( {Z}_N={S}_N/\sqrt{\mathbf{V}{S}_N} \) with variances VS N  > 0 (S N  = X1 + ⋯ + X N ) of centered strongly mixing or uniformly strongly mixing random variables X1, X2, . . . . Here the number of summands N is a nonnegative integer-valued random variable independent of X1,X2, . . . .

Keywords

central limit theorem random sum normal approximation strongly mixing random variables uniformly strongly mixing random variables τ-shifted distributions 

MSC

60F05 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Data Science and Digital TechnologiesVilnius UniversityVilniusLithuania

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