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Improvement of the non-uniform version of Berry-Esseen inequality via Paditz-Siganov theorems. (English) Zbl 1136.60018
Summary: We improve the constant in a non-uniform bound of the Berry-Esseen inequality without assuming the existence of the absolute third moment by using the method obtained from the Paditz-Siganov theorems. Our bound is better than the results of P. Thongtha and K. Neammanee [Thai Journal of Mathematics 5, 1–13 (2007)].
MSC:
60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
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