Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method
Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method
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DOI：
10.1214/aop/1176989531
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发表时间：
1992-10
影响因子：
2.3
通讯作者：
A. Barbour;Louis H. Y. Chen;Wei-Liem Loh
中科院分区：
文献类型：
--
作者：
A. Barbour;Louis H. Y. Chen;Wei-Liem Loh
本文的目的是将Stein方法推广到复合Poisson分布情形。这里关注的复合泊松分布是POIS$（\nu）$的形式，其中$\nu$是$（0，\infty）$上的有限正测度。建立了一些与这些分布相关的结果。这些反过来又被用在一些例子中，以给出在复合泊松近似的随机变量的总和分布的错误的界限。
The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS$(\nu)$, where $\nu$ is a finite positive measure on $(0, \infty)$. A number of results related to these distributions are established. These in turn are used in a number of examples to give bounds for the error in the compound Poisson approximation to the distribution of a sum of random variables.