标题： 二项随机变量比值的极限分布 显示英文标题

标题： Limiting distributions of ratios of Binomial random variables

摘要： 我们研究了量$X^s/(X+Y)^r$的极限分布，其中$X$和$Y$是两个独立的具有相同成功概率和试验次数$n$和$m$的二项随机变量，且$r,s$为正实数。 在若干设定下，我们证明该量收敛于一个具有特定均值和方差的正态分布，并通过模拟展示了这些理论结果。 显示英文摘要

摘要： We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive real numbers. Under several settings, we prove that this converges to a Normal distribution with a given mean and variance, and demonstrate these theoretical results through simulations.