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The rate of convergence to the normal law in terms of pseudomoments
Volume 2, Issue 2 (2015), pp. 95–106
Yuliya Mishura   Yevheniya Munchak   Petro Slyusarchuk  

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https://doi.org/10.15559/15-VMSTA23
Pub. online: 21 April 2015      Type: Research Article      Open accessOpen Access

Received
21 February 2015
Revised
4 April 2015
Accepted
10 April 2015
Published
21 April 2015

Abstract

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting estimates of the rate of convergence of the order higher than ${n}^{-1/2}$.

References

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Honak, S.V., Sytar, I.V., Slyusarchuk, P.V.: On one estimate due to Yu.P. Studnev. In: Proceedings of the Student Research Conference of the Mathematical Faculty of UzhNu. Series Mathematics and Applied Mathematics, p. 92 (2013) (in Ukrainian)
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Statulevičius, V.A.: Limit theorems for densities and asymptotic expansions for the distributions of sums of independent random variables. Theory Probab. Appl. 10(4), 582–595 (1965). MR0193660
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Studnyev, Y.P.: One form of estimating the rate of convergence to a normal law. Ukr. Math. J. 20, 256–259 (1968)
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Zolotarev, V.M.: On the closeness of the distributions of two sums of independent random variables. Theory Probab. Appl. 10, 472–479 (1965). MR0189109
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Zolotarev, V.M.: Exactness of an approximation in the central limit theorem. In: Proc. 2nd Japan–USSR Sympos. Probab. Theory, Kyoto 1972. Lect. Notes Math., vol. 330, pp. 531–543 (1973). MR0443048
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Zolotarev, V.M.: Modern Theory of Summing the Independent Random Variables. Nauka, Moscow (1986). MR0917274

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Keywords
Rate of convergence truncated pseudomoments Gaussian distribution

MSC2010
60E05 60F05

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