Geodesic
The Chebyshev--Edgeworth correction in the central limit theorem for integer-valued independent summands
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 676-692

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We give a short overview of the results related to the refined forms of the central limit theorem, with a focus on independent integer-valued random variables (r.v.'s). In the independent and non-identically distributed (non-i.i.d.) case, an approximation is then developed for the distribution of the sum by means of the Chebyshev–Edgeworth correction containing the moments of the third order.
Keywords: central limit theorem, the Chebyshev–Edgeworth correction, integer-valued random variables. 
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     author = {S. G. Bobkov and V. V. Ulyanov},
     title = {The {Chebyshev--Edgeworth} correction in the central limit theorem for integer-valued independent summands},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a3/}
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S. G. Bobkov; V. V. Ulyanov. The Chebyshev--Edgeworth correction in the central limit theorem for integer-valued independent summands. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 676-692. http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a3/