对${\mathit{\Phi }}_{\alpha }$-极值吸引场$(\alpha >0)$的随机样本及 非随机样本的次序统计量的精致 渐近性进行了讨论,得到非随机样本的次序统计量的精致渐近性的结果是 随机样本的结果当$\lambda =1$时的特况, 特别地当$p=r$时两者的结果是完全一致的.

In this paper, we discuss the precise asymptotics for order statistics of a random sample and a non-random sample that belong to the maximum domain of attraction(MDA) of ${\mathit{\Phi }}_{\alpha }$ for $\alpha >0$. It can be sees that the result of precise asymptotics for order statistics of a non-random sample is the particular case of the result for random sample when $\lambda =1$. Particularly, when $p=r$, the results are the same.