A Generalization of the Wang–Ahmad Inequality

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...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 237; no. 5; pp. 646 - 651
Main Authors Gabdullin, R. A., Makarenko, V.A., Shevtsova, I. G.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.03.2019
Springer
Springer Nature B.V
Subjects
Equality
Independent variables
Mathematics
Mathematics and Statistics
Probability distributions
Random variables
Online AccessGet full text

Cover

More Information
Summary: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).
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04190-4