论文标题
Stein的分发方法建模竞争和互补风险问题
Stein's method for distributions modelling competing and complementary risk problems
论文作者
论文摘要
竞争和互补风险（CCR）问题通常是使用最大或最小值的一类分布进行建模的。随机变量；我们将此类称为CCR类的分布类。尽管CCR分布通常没有易于计算的密度或概率质量函数，但两种特殊情况，即泊松指数和指数几何分布，可以轻松计算。因此，使用这些简单分布的近似CCR分布是有意思的。在本文中，我们开发了Stein的CCR类别分布类别的方法，以提供一种一般比较方法，以绑定两个CCR分布之间的距离，并将这种方法与使用Lindeberg参数获得的界限进行对比。我们详细介绍了泊松指数和指数几何分布的比较。
Competing and Complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of i.i.d. random variables; we call this class the CCR class of distributions. While the CCR distributions generally do not have an easy-to-calculate density or probability mass function, two special cases, namely the Poisson-exponential and the exponential geometric distributions, can easily be calculated. Hence, it is of interest to approximate CCR distributions with these simpler distributions. In this paper, we develop Stein's method for the CCR class of distributions to provide a general comparison approach to bound the distance between two CCR distributions and contrast this approach to bounds obtained using a Lindeberg argument. We detail the comparison for Poisson-exponential and exponential-geometric distributions.
