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On large deviations of sums of independent random variables. (English) Zbl 1125.60024
Summary: Extensions of some limit theorems are proved for tail probabilities of sums of independent identically distributed random variables satisfying the one-sided or two-sided Cramér’s condition. The large deviation \(x\)-region under consideration is broader than in the classical Cramér’s theorem, and the estimate of the remainder is uniform with respect to \(x\). The corresponding asymptotic expansion with arbitrarily many summands is also obtained.

MSC:
60F10 Large deviations
60G50 Sums of independent random variables; random walks
62E20 Asymptotic distribution theory in statistics
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References:
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