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On the normal approximation of a binomial random sum. (English) Zbl 1296.60065

Summary: We present upper bounds of the \(L_{s}\) norms of the normal approximation for random sums of independent identically distributed random variables \(X_{1}, X_{2}, \dots\) with finite absolute moments of order \(2 + \delta, 0 < \delta \leqslant 1\), where the number of summands \(N\) is a binomial random variable independent of the summands \(X_{1}, X_{2}, \dots\). The upper bounds obtained are of order \((\mathbf EN)^{-\delta/2}\) for all \(1 \leqslant s \leqslant \infty\).

MSC:

60F05 Central limit and other weak theorems
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