We derive strong laws of large numbers and central limit theorems for Bajraktarević, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed.

我们为 Bajraktarević、Gini 和指数（也称为 Beta 型）和独立同分布 (iid) 随机变量的对数柯西商均值推导出强数定律和中心极限定理。一系列 iid 随机变量的指数和对数柯西商均值在通常的平方根标度下表现为渐近正态，就像给定随机变量的几何均值一样。有点令人惊讶的是，iid 随机变量的乘法柯西商均值以一种相当不同的方式渐近地表现：为了获得非平凡的正态极限分布，需要时间相关的中心化。