论文标题
中央限制定理的变化和第一类的stirl数字
Variations of Central Limit Theorems and Stirling numbers of the First Kind
论文作者
论文摘要
我们构建了双序列的新参数化$ \ {a_ {n，k}（s）\} _ {n，k} $之间的$ a_ {n，k}（n，k}（0）= \ binom {n-1} {n-1} {k-1} {k-1} {k-1} $ \ frac {1} {n！} \ stirl {n} {k} $，其中$ \ stirl {n} {k} {k} $是第一类无签名的stirling号码。对于每个$ s $，我们证明了中心限制定理和本地限制定理。这扩展了de \ moivre-laplace中心限制定理和贡查洛夫的结果，即第一类的未签名的stirling数字在渐近上是正常的。在此，我们提供了几种应用程序。
We construct a new parametrization of double sequences $\{A_{n,k}(s)\}_{n,k}$ between $A_{n,k}(0)= \binom{n-1}{k-1}$ and $A_{n,k}(1)= \frac{1}{n!}\stirl{n}{k}$, where $\stirl{n}{k}$ are the unsigned Stirling numbers of the first kind. For each $s$ we prove a central limit theorem and a local limit theorem. This extends the de\,Moivre--Laplace central limit theorem and Goncharov's result, that unsigned Stirling numbers of the first kind are asymptotically normal. Herewith, we provide several applications.
