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On the accuracy of normal approximation for distributions of random sums with infinitely divisible indices. (English. Russian original) Zbl 0895.60026

Theory Probab. Appl. 41, No. 4, 798-805 (1996); translation from Teor. Veroyatn. Primen. 41, No. 4, 920-926 (1996).
Summary: Random sums of independent identically distributed random variables with indices having infinitely divisible (and hence, compound Poisson) distributions are considered. Estimates of the accuracy of the normal approximation to the distributions of these random sums are obtained. In the right-hand sides of these estimates there are “noncentral” Lyapunov fractions. The problem of relationship between “classical” and “noncentral” Lyapunov fractions is discussed. It is demonstrated that the use of the latter is more natural within the problem under consideration.

MSC:

60F05 Central limit and other weak theorems
60E07 Infinitely divisible distributions; stable distributions