Journal of Mathematical Sciences

, Volume 237, Issue 6, pp 775–781 | Cite as

A Generalization of the Rozovskii Inequality

  • R. A. Gabdullin
  • V.A. Makarenko
  • I. G. ShevtsovaEmail author

Adopting ideas of Katz (1963), Petrov (1965), Wang and Ahmad (2016), and Gabdullin, Makarenko, and Shevtsova (2016), we generalize the Rozovskii inequality (1974) which provides an estimate of the accuracy of the normal approximation to distribution of a sum of independent random variables in terms of the absolute value of the sum of truncated in a fixed point third-order moments and the sum of the second-order tails of random summands. The generalization is due to introduction of a truncation parameter and a weighting function from a set of functions originally introduced by Katz (1963). The obtained inequality does not assume finiteness of moments of random summands of order higher than the second and may be even sharper than the celebrated inequalities of Berry (1941), Esseen (1942, 1969), Katz (1963), Petrov (1965), and Wang & Ahmad (2016).


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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 Science, Hangzhou 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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