论文标题
与$ m $相关的随机变量的总和有关的近似值
Approximations Related to the Sums of $m$-dependent Random Variables
论文作者
论文摘要
在本文中，我们考虑了符合$ m $依赖性随机变量的非负整数的总和，及其与功率序列分布的近似值。我们首先讨论了功率序列分布的一些相关结果，例如Stein operator，Stein方程解决方案等上的均匀和非统一边界等。使用Stein的方法，我们获得了所考虑的近似问题的误差界限。作为特殊情况，我们讨论了两个应用程序，即$ 2 $ -runs和$（k_1，k_2）$ - 运行并将界限与现有界限进行比较。
In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein operator, uniform and non-uniform bounds on the solution of Stein equation, and etc. Using Stein's method, we obtain the error bounds for the approximation problem considered. As special cases, we discuss two applications, namely, $2$-runs and $(k_1,k_2)$-runs and compare the bound with the existing bounds.
