Poisson approximations in selected metrics by coupling and semigroup methods with applications |
| |
Institution: | 1. Computer Science Department, University of Central Arkansas, United States;2. School of Computer Science and Engineering, Nanjing University of Science and Technology, China |
| |
Abstract: | Let Sn = X1 + … + Xn, where X1,…, Xn are independent Bernoulli random variables. In this paper, we evaluate probability metrics of the Wasserstein type between the distribution of Sn and a Poisson distribution. Our results show that, if E(Sn) = O(1) and if the individual probabilities of success of the Xi's tend uniformly to zero, then the general rate of convergence of the above mentioned metrics to zero is O(∑ni = 1P2i). We also show that this rate is sharp and discuss applications of these results. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|