Cauchy抽样下集中式$r$的渐近分布
Asymptotic Distribution of Centralized $r$ When Sampling from Cauchy
摘要：
假设$X$和$Y$是独立的随机变量，每个都具有带有已知中值的柯西分布。取每个$X$和$Y$的大小为$n$的随机独立样本，然后可以计算它们的集中经验相关系数$r$。分析研究这个$r$的抽样分布似乎只可能在大的$n$限制，这就是我们在这篇文章中所做的，得出几个新的和有趣的结果。
英文摘要：
Assume that $X$ and $Y$ are independent random variables, each having a Cauchy distribution with a known median. Taking a random independent sample of size $n$ of each $X$ and $Y$, one can then compute their centralized empirical correlation coefficient $r$. Analytically investigating the sampling distribution of this $r$ appears possible only in the large $n$ limit; this is what we have done in this article, deriving several new and interesting results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
