A note on characterizations of G-normal distribution

摘要

In this paper, we show that the G-normality of X and Y can be characterizedaccording to the form of f such that the distribution of{\lambda}+f({\lambda})Y does not depend on {\lambda}, where Y is an independentcopy of X and {\lambda} is in the domain of f. Without the condition that Y isidentically distributed with X, we still have a similar argument.