Generalized definition of the geometric mean of a non negative random variable

被引：9

作者：

Feng, Changyong ^{[1
,2
]}

Wang, Hongyue ^{[1
]}

Zhang, Yun ^{[1
]}

Han, Yu ^{[1
]}

Liang, Yuefeng ^{[3
]}

Tu, Xin M. ^{[1
]}

机构：

[1] Univ Rochester, Dept Biostat & Computat Biol, 601 Elm Ave,Box 630, Rochester, NY 14642 USA

[2] Univ Rochester, Dept Anesthesiol, Rochester, NY USA

[3] Univ Chicago, Dept Stat, Chicago, IL 60637 USA

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2017年 / 46卷 / 07期

关键词：

Dominated convergence theorem; Geometric mean; Log-transformation;

D O I：

10.1080/03610926.2015.1066818

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：

The first probabilistic definition of the geometric mean of a non negative random variable under certain assumptions was given in Feng et al. (2013). In this paper, we generalize the definition to a larger class of random variables. We also show the basic properties of the geometric mean and point out its discontinuity and instability. Some convergence properties are studied as well, for which we emphasize its link to the positive moments of the random variable. A discussion of potential applications of the new definition in biomedical research and open questions to complete the theory of geometric mean is highlighted.

引用

页码：3614 / 3620

页数：7

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