Article PDF
Avoid common mistakes on your manuscript.
References
Baum, L. E., and M. L. Katz: On the influence of moments on the asymptotic distribution of sums of random variables. Ann. math. Statistics 34, 1042–1044 (1963).
Bikjalis, A.: An estimate for the remainder term in the central limit theorem (Russian, English summary). Litovsk. Mat. Sbornik 4, 303–308 (1964).
Feller, W.: An introduction to probability theory and its applications, Vol. II. New York: Wiley 1966.
Heyde, C. C.: Some results on small deviation probability convergence rates for sums of independent random variables. Canadian J. Math. 18, 656–665 (1966).
Ibragimov, I. A.: The rate of convergence to the normal distribution. Soviet Math. Doklady 6, 580–582 (1965).
Katz, M. L.: Note on the Berry-Esseen theorem. Ann. math. Statistics 34, 1107–1108 (1963).
Linnik, Yu. V., and I. A. Ibragimov: Independent and stationary dependent random variables (Russian). Moscow 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heyde, C.C. On the influence of moments on the rate of convergence to the normal distribution. Z. Wahrscheinlichkeitstheorie verw Gebiete 8, 12–18 (1967). https://doi.org/10.1007/BF00533941
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00533941