On a limit theorem for a non-linear scaling (Q2244576)

In this short note, positive random variables are normalized by a non-linear shrinking transformation (s-operation), \(\max\{0, x-r\}\), and then partial sums are computed. A limit theorem for those sums is proved for non-negative independent and identically distributed variables. The main result is interesting. A historical note on the s-operations is also given.