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A Generalization of the Wang–Ahmad Inequality

  • R. A. Gabdullin
  • V.A. Makarenko
  • I. G. ShevtsovaEmail author
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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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • R. A. Gabdullin
    • 2
  • V.A. Makarenko
    • 2
  • I. G. Shevtsova
    • 1
    • 2
    • 3
    Email author
  1. 1.School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia
  3. 3.Institute of Informatics Problems of Federal Research Center “Computer Science and Control”Russian Academy of SciencesMoscowRussia

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