幂赋范下的极值大偏差

On Large Deviation of Extremes under Power Normalization

(Xn,n≥1)为独立同分布随机变量序列,Mn=max(X1,…,Xn).本文在二阶广义正规变换函数条件下得到了幂赋范情形中Mn分布更为精确的一致渐近展开,以及相应的更为精确的极值大偏差结果.

Let （Xn,n≥1） be a sequence of independent and identically distributed discrete random variable, denoted by Mn=max（X1,…,Xn）, the partial maximum. In this note, an improved uniform approxima- tion of the distribution of Mn with second order extended regularly varying condition under power normali- zation is derived, which implies a general result about large deviations of Mn under power normalization.