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October, 1975 Generalisation and Application of Some Results of Ibragimov on Convergence to Normality
Julian Leslie
Ann. Probab. 3(5): 897-902 (October, 1975). DOI: 10.1214/aop/1176996279


We modify certain results obtained by I. A. Ibragimov concerning the remainder term in the Central Limit Theorem and the remainder term in the approximation of the distribution function for normed sums of i.i.d. rv's by a portion of the Chebyshev series and we then use these to complete some results appearing in a joint article by C. C. Heyde and the author (Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 21 255-268) (as well as in a similar article by F. N. Galstian (Theor. Probability Appl. 16 3, 528-533)).


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Julian Leslie. "Generalisation and Application of Some Results of Ibragimov on Convergence to Normality." Ann. Probab. 3 (5) 897 - 902, October, 1975.


Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0322.60022
MathSciNet: MR402863
Digital Object Identifier: 10.1214/aop/1176996279

Primary: 60G50
Secondary: 60E05

Keywords: central limit theorem , Chebyshev series approximation , Convergence rates

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 5 • October, 1975
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