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This article is cited in 13 scientific papers (total in 13 papers)
A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III
G. P. Chistyakov Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
Abstract:
A new asymptotic expansion is obtained in Lyapunov's central limit theorem for distribution functions of centered and normed sums of independent random variables which are not necessary identically distributed. It is applied to determine the asymptotically best constants in the Berry–Esseen inequality, thus solving problems of their optimal values raised by Kolmogorov and Zolotarev.
Keywords:
central limit theorem, Lyapunov's theorem, Berry–Esseen bounds, asymptotic expansion, characteristic functions.
Received: 30.06.1998
Citation:
G. P. Chistyakov, “A new asymptotic expansion and asymptotically best constants in Lyapunov's theorem. III”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 475–497; Theory Probab. Appl., 47:3 (2003), 395–414
Linking options:
https://www.mathnet.ru/eng/tvp3677https://doi.org/10.4213/tvp3677 https://www.mathnet.ru/eng/tvp/v47/i3/p475
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