北京大学学报（自然科学版）

伴随极值分布函数的弱收敛

程士宏   

  1. 北京大学数学科学学院，北京，100871
  • 收稿日期:1998-10-27 出版日期:2000-01-20 发布日期:2000-01-20

Weak Convergence for Distribution Functions of Induced Maximum

CHENG Shihong   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1998-10-27 Online:2000-01-20 Published:2000-01-20

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摘要： 设{(Xn,Yn)}是i.i.d.随机向量序列，共同d.f.为F。本文在更弱的条件下证明了An-1(Y(n, n)-Bn)→I对某准d.f.I成立，从而推广了Nagaraja和David的结果。此外还指出：对于(an-1(Xn, n-bn),An-1(Y(n, n)-Bn))的联合分布的弱收敛，本文的条件不仅充分，而且必要。最后，揭露了二元极值弱收敛与(an-1 (Xn, n-bn), An-1 (Y(n, n)-Bn))的联合分布弱收敛之间的紧密联系。

关键词: 伴随极值, 分布函数的弱收敛, 二元极值

Abstract: Let{(Xn,Yn)} be i.i.d. random vectors with common d.f. F. Under weaker conditions, it is shown in this paper that An-1(Y(n, n)-Bn)→I holds for some nondecreasing function I. Therefore the Nagaraja and David's result is generalized. Moreover, We prove that our conditions are not only sufficient, but also necessary for weak convergence of the sequence (an-1(Xn, n-bn), An-1(Y(n, n)-Bn)). At last, we show that the weak convergences of bivariate extreme values and (an-1 (Xn, n-bn), An-1(Y(n, n)-Bn)) are closely related.

Key words: induced maximum, weak convergence for distribution functions, bivariate extremes

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