Theory of Probability &Its Applications, Volume 66, Issue 1, Page 121-141, January 2021.
In this paper we modify the Stein method and the auxiliary technique of distributional transformations of random variables. This enables us to estimate the convergence rate of distributions of normalized geometric sums to the Laplace law. For independent summands, the developed approach provides an optimal estimate involving the ideal metric of order 3. New results are also obtained for the Kolmogorov and Kantorovich metrics.

中文翻译：

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随机几何和分布对拉普拉斯定律的收敛率

Theory of Probability & Its Applications，第 66 卷，第 1 期，第 121-141 页，2021
年1 月。在本文中，我们修改了 Stein 方法和随机变量分布变换的辅助技术。这使我们能够估计归一化几何和的分布对拉普拉斯定律的收敛速度。对于独立的被加数，所开发的方法提供了涉及 3 阶理想度量的最佳估计。还获得了 Kolmogorov 和 Kantorovich 度量的新结果。