中文摘要：

设{Xk,1≤k≤n}独立同分布,X（1）,X（2）,…,X（n）为其顺序统计量.当总体服从艾拉姆咖分布时,首先得到了其顺序统计量的联合概率密度函数、极端顺序统计量的密度函数,进一步说明了极端顺序统计量的概率密度可以表示为一系列参数不同的伽玛分布密度的线性组合.其次给出了极差Rn的概率分布和高阶原点矩的精确表达式.最后还研究了极端顺序统计量X（1）和X（n）的渐近性质.

英文摘要：

Let {Xk,1≤k≤n} be independent and identically distributed random variables,X（1）,X（2）,…,X（n） be their order statistics. Firstly the joint probability density function of its order statistics and the probability density functions of extreme order statistics were given when the population followed Эрланга distribution, to further illustrate that the probability density of extreme order statistics can be expressed as a linear combination of a series of gamma distribution density with different parameters. Secondly the probability distribution of extremely range were derived when the population followed Эрланга distribution, the explicit formulas for the higher origin moment about extremely range Rn was also obtained. Finally, the asymptotic properties of the extreme order statistics X（1） and X（n） were discussed.