By introducing a truncation parameter, we generalize the Ahmad–Wang inequality (2016) which provides an estimate of the accuracy of the normal approximation to distribution of a sum of independent random variables in terms of weighted absolute values of truncated third-order moments and tails of the second-order moments of random summands. The obtained estimate also generalizes the celebrated inequalities due to Berry (1941), Esseen (1942, 1969), Katz (1963), and Petrov (1965).
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Debrecen, Hungary, August 25–29, 2017. Part I
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Gabdullin, R.A., Makarenko, V. & Shevtsova, I.G. A Generalization of the Wang–Ahmad Inequality. J Math Sci 237, 646–651 (2019). https://doi.org/10.1007/s10958-019-04190-4
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DOI: https://doi.org/10.1007/s10958-019-04190-4