We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5562838 | PMC |
| http://dx.doi.org/10.1186/s13660-017-1468-y | DOI Listing |
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