On exact strong laws of large numbers for ratios of random variables and their applications

被引：5
|
作者：
Matula, Przemyslaw [1 ]
Adler, Andre [2 ]
Kurasinski, Pawel [1 ]
机构：
[1] Marie Curie Sklodowska Univ, Inst Math, Dept Math Stat, Pl MC Sklodowskiej 1, PL-20031 Lublin, Poland
[2] IIT, Dept Math, Chicago, IL 60616 USA
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2020年 / 49卷 / 13期
关键词：
Almost sure convergence; strong law of large numbers; exact laws; order statistics; ORDER-STATISTICS;
D O I：
10.1080/03610926.2019.1586935
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the almost sure convergence of weighted sums of ratios of independent random variables satisfying some general, mild conditions. The obtained results are applied to exact laws for order statistics. An exact law for independent random variables which are nonidentically distributed is also proved and applied to ratios of adjacent order statistics for a sample of uniformly distributed random variables.
引用
收藏
页码：3153 / 3167
页数：15
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