Error estimate in the central limit theorem

Aurelija  Kasparavičiūtė; Kazimieras  Padvelskis

doi:10.15388/LMR.2008.18129

Articles

Aurelija Kasparavičiūtė

Vytautas Magnus University

Kazimieras Padvelskis

Vytautas Magnus University

Published 2008-12-21

https://doi.org/10.15388/LMR.2008.18129

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Keywords

the Central limit theorem
normal distribution
error estimate
cumulants

How to Cite

Kasparavičiūtė, A. and Padvelskis, K. (2008) “Error estimate in the central limit theorem”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 389–394. doi:10.15388/LMR.2008.18129.

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Abstract

In this paper, we determined, independent identically distributed random variable’s {X_k, k = 1,2,...} centered and normalized sum’s S_n= \sumⁿ _k₌₁X_kdistribution’s F_n(x) = P(Z_n< x) exact error estimate in case of the normal approximation with one Cebyšova’s asymptotic expansion’s term.

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