The asymptotic distributions of sums of record values for distributions with lognormal-type tails

被引：0

作者：

Hu, ZS ^{[1
]}

Su, C

Wang, DC

机构：

[1] Univ Sci & Technol China, Dept Stat & Finance, Hefei 230026, Peoples R China

[2] Univ Elect Sci China, Dept Appl Math, Chengdu 650054, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2002年 / 45卷 / 12期

关键词：

limit distribution; lognormal; record; regular variable; slowly varying;

D O I：

10.1360/02ys9167

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X-1, X-2,... be a sequence of i.i.d. random variables and let X-(1), X-(2),... be the associated k for record value sequence. We focus on the asymptotic distributions of sums of records, T-n = Sigma(k=1)(n) X-1 is an element of LN(gamma). In this case, we find that 2 is a strange point for parameter gamma. When gamma > 2, T-n is asymptotically normal, while for 2 > gamma > 1, we prove that T-n cannot converge in distribution to any non-degenerate law through common centralizing and normalizing and log T-n is asymptotically normal.

引用

页码：1557 / 1566

页数：10