Shorgin, S. Ya. 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. Cited in 3 Documents MSC: 60F05 Central limit and other weak theorems 60E07 Infinitely divisible distributions; stable distributions Keywords:random sums; index and random summands of a random sum; noncentral and classical Lyapunov ratios; infinitely divisible distribution; Poisson and compound Poisson distributions; normal approximation × Cite Format Result Cite Review PDF