Abstract
This paper contains a connection between the well-known Berry Esseen inequality for the uniform distance between two distributions (theorem A) and Zolotarev's inequality for the Levy distance between two distributions ([3]), theorem B). More precisely we give an inequality (theorem 1), from which both inequalities follow, as well as Fainleib's inequality (theorem C). Our estmations use the second modulus of smoothness of the distributions.
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References
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© 1987 Springer-Verlag
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Popov, V.A. (1987). On the inequalities of Berry-Esseen and V.M. Zolotarev. In: Kalashnikov, V.V., Penkov, B., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072717
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DOI: https://doi.org/10.1007/BFb0072717
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