论文标题
两个经典泊松限制法律的扩展到非平稳独立数据
Extensions of two classical Poisson limit laws to non-stationary independent data
论文作者
论文摘要
在概率理论的渐近方法简介中的较早阶段中，序列的弱收敛性$（x_n）_ {n \ geq 1} $的随机变量的二项式（\ textit {rv}）与Poisson定律是经典和易于prove。关于序列的结果的一个版本$（y_n）_ {n \ geq 1} $ of binmial \ textit {rv}也存在。在这两种情况下，$ x_n $和$ y_n-n $均为$ s_n [x] $和$ s_n [y] ber uloulli \ textit {rv}的阵列，分别校正了几何\ textit \ textit {rv}。如果在\ textit {rv}阵列的渐近定理的一般框架中考虑，则可以将这两个简单的结果推广到非平台数据及以外的非平台和依赖数据。进一步的概括提供了有趣的结果，直接方法无法找到。在本文中，我们专注于对非平稳独立数据的概括。稍后将解决依赖数据的扩展。
In earlier stages in the introduction to asymptotic methods in probability theory, the weak convergence of sequences $(X_n)_{n\geq 1}$ of Binomial of random variables (\textit{rv}'s) to a Poisson law is classical and easy-to prove. A version of such a result concerning sequences $(Y_n)_{n\geq 1}$ of negative binomial \textit{rv}'s also exists. In both cases, $X_n$ and $Y_n-n$ are by-row sums $S_n[X]$ and $S_n[Y]$ of arrays of Bernoulli \textit{rv}'s and corrected geometric \textit{rv}'s respectively. When considered in the general frame of asymptotic theorems of by-row sums of \textit{rv}'s of arrays, these two simple results in the independent and identically distributed scheme can be generalized to non-stationary data and beyond to non-stationary and dependent data. Further generalizations give interesting results that would not be found by direct methods. In this paper, we focus on generalizations to the non-stationary independent data. Extensions to dependent data will addressed later.
