混合对数正态分布最大值的极限分布

The Limiting Distributions of Maxima for Mixed Logarithm Normal Distributions

设{Xn,n≥1}是独立同分布的随机变量序列,并且每个随机变量Xn服从混合对数正态分布.Mn=max{Xk,1≤k≤n}表示{Xn,n≥1}的部分最大值,同服从混合对数正态分布的独立随机变量最大值的极限分布以及相应的赋范常数.

Let { Xn,n ≥ 1 } be a seguence of independent and identically distributed random variables with each Xn following mixed logarithm normal distribution.Let Mn =max [Xk,1 ≤ k ≤ n } denote the partial maximum of { Xn,n ≥ 1 }.In this paper,the limiting distributions of extremes of independent identically distributed random variables with mixed logarithm normal distribution and corresponding norming constants are studied.