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

被引：0

作者：

Hu, Zhishui

Su, Chun

Wang, Dingcheng

机构：

[1] Department of Statistics and Finance, Univ. of Sci. and Technol. of China, Hefei 230026, China

[2] Applied Mathematical Department, Univ. of Electric Science of China, Chengdu 650054, China

来源：

Science in China, Series A: Mathematics, Physics, Astronomy | 2002年 / 45卷 / 12期

基金：

中国国家自然科学基金;

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摘要：

Let X1, X2, ... be a sequence of i.i.d. random variables and let X(1), X(2), ... be the associated record value sequence. We focus on the asymptotic distributions of sums of records, Tn = summation nk = 1 X(k), for X1 is a member of the set of LN (γ). In this case, we find that 2 is a strange point for parameter γ. When γ > 2, Tn is asymptotically normal, while for 2 > γ > 1, we prove that Tn cannot converge in distribution to any non-degenerate law through common centralizing and normalizing and log Tn is asymptotically normal.

引用

页码：1557 / 1566