In this note we proved that weak limits, of sums of positive, independent and identically distributed random variables which are re-normalized by a non-linear shrinking transform $max(0,x-r)$, are either degenerate or (some) compound Poisson distributions.

中文翻译：

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关于非线性标度的极限定理

在本笔记中，我们证明了通过非线性收缩变换重新归一化的正、独立和同分布随机变量之和的弱极限 $最大限度(0,X-r)$, 要么是退化的，要么是（一些）复合泊松分布。