On the accuracy of the normal approximation to the distributions of Poisson random sums |
| |
| Authors: | Irina Shevtsova |
| |
| Institution: | Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Mathematical Statistics, Moscow, Russia |
| |
| Abstract: | The analogue of the Berry–Esseen inequality for Poisson random sums is improved in 4–11 times depending on the maximal order 2 < s ≤ 3 of the finite absolute moment of the distribution of random summands. For the case, when s = 3, under additional assumption concerning the smoothness of distribution of summands we also obtained in some sense unimprovable estimate consisting of two summands: the first summand being the noncentral Lyapunov fraction with the coefficient equal to the unimprovable asymptotically exact constant and the second one decreases faster. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
| |
| Keywords: | |
|
|
