Email this article A Generalization of the Wang–Ahmad Inequality
- Authors: Gabdullin R.A.1, Makarenko V.1, Shevtsova I.G.2,1,3
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics, Moscow State University
- School of Science, Hangzhou Dianzi University
- Institute of Informatics Problems of Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
- Issue: Vol 237, No 5 (2019)
- Pages: 646-651
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242419
- DOI: https://doi.org/10.1007/s10958-019-04190-4
- ID: 242419
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Abstract
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).
About the authors
R. A. Gabdullin
Faculty of Computational Mathematics and Cybernetics, Moscow State University
Email: ishevtsova@cs.msu.ru
Russian Federation, Moscow
V.A. Makarenko
Faculty of Computational Mathematics and Cybernetics, Moscow State University
Email: ishevtsova@cs.msu.ru
Russian Federation, Moscow
I. G. Shevtsova
School of Science, Hangzhou Dianzi University; Faculty of Computational Mathematics and Cybernetics, Moscow State University; Institute of Informatics Problems of Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
Author for correspondence.
Email: ishevtsova@cs.msu.ru
China, Hangzhou; Moscow; Moscow
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