This article is cited in 3 papers

Estimates for convergence rate of distributions of random sums with infinitely divisible indices to the normal distribution

S. V. Gavrilenko

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: New estimates for convergence rate of distributions of random sums with infinitely divisible indices were obtained. These estimates remain true under weaker conditions than the known ones. As an example of this result, the article contains estimates of the accuracy of the normal approximation for the distribution functions of random sums with indices that have negative binomial distribution.

Keywords: random sum; integer-valued infinitely divisible distribution; generalized Poisson distribution; negative binomial distribution; normal approximation.