Abstract
The problem of estimation of deviation of the distribution of the sum of a random number of differently distributed random variables from the normal distribution is considered, i.e., the Esseen inequality for distributions of random sums is established. As a particular case, the Berry-Esseen inequality is obtained.
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Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 143–146, July, 1977.
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Batirov, K., Manevich, D.V. & Nagaev, S.V. The Esseen inequality for sums of a random number of differently distributed random variables. Mathematical Notes of the Academy of Sciences of the USSR 22, 569–571 (1977). https://doi.org/10.1007/BF01147702
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DOI: https://doi.org/10.1007/BF01147702