M. E. Grigor'eva, I. G. Shevtsova, “An improvement of the Katz–Berry–Esseen inequality”, Inform. Primen., 2010, Volume 4, Issue 2,Pages <nobr>75

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An improvement of the Katz–Berry–Esseen inequality

M. E. Grigor'eva, I. G. Shevtsova

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The upper estimates of the absolute constant in the Katz–Berry–Esseen inequality for sums of independent identically distributed random variables with finite absolute moments of order between 2 and 3 are sharpened and an alternative inequality with sharpened structure and evaluated constants is proposed.

Keywords: central limit theorem; Katz–Berry–Esseen inequality; Lyapounov fraction.