It is long known that the distribution of a sum S_n of independent non-negative integer-valued random variables can often be approximated by a Poisson law: S_n≈π_λ, where . The problem of evaluating the accuracy of such approximation has attracted a lot of attention in the past six decades. From a practical point of view, the problem has important applications in insurance, reliability theory, extreme value theory, etc.; from a theoretical point of view, it provides insights into Kolmogorov’s problem.

Among popular metrics considered in the literature is the Gini–Kantorovich distance d_G. The task of establishing an estimate of d_G(S_n;π_λ) with correct (the best possible) constant at the leading term remained open for a long while.

The paper presents a solution to that problem. A first-order asymptotic expansion is established as well. We show that the accuracy of approximation can be considerably better if the random variables obey an extra condition involving the first two moments. A sharp estimate of the accuracy of shifted (translated) Poisson approximation is established as well.

据早就知道的总和的分布š _Ñ独立非负整数值的随机变量通常可以通过泊松法来近似：小号_Ñ听，说：π _λ，其中。在过去的六十年中，评估这种近似的准确性问题引起了很多关注。从实践的角度来看，该问题在保险，可靠性理论，极值理论等方面具有重要的应用。从理论上讲，它提供了对科尔摩哥罗夫问题的见解。

在文献考虑流行度量是基尼的Kantorovich距离ð _ģ。建立的估计的任务d _ģ（小号_Ñ ; π _λ）与正确的（最好可能的）在前缘术语恒定保持开放了很长一段时间。

本文提出了解决该问题的方法。一阶渐近展开也被建立。我们表明，如果随机变量服从涉及前两个时刻的额外条件，则逼近的准确性会好得多。还建立了移位（平移）泊松近似精度的精确估计。