Harmonic mean and geometric mean of a non negative random variable

被引：0

作者：

Feng, Changyong ^{[1
]}

Wang, Hongyue ^{[2
]}

机构：

[1] Univ Rochester, Dept Biostat & Computat Biol, Rochester, NY 14627 USA

[2] Univ Rochester, Dept Anesthesiol & Perioperat Med, Rochester, NY USA

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2025年 / 54卷 / 06期

关键词：

Dominated convergence theorem; geometric mean; harmonic mean;

D O I：

10.1080/03610926.2024.2349713

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：

In this article, we define the harmonic mean of a non negative random variable, reconstruct the famous HM-GM-AM inequality, and explore some convergence results related to these mean values.

引用

页码：1805 / 1812

页数：8

共 8 条

[1] LORENZ ORDERING OF MEANS AND MEDIANS [J].

ARNOLD, BC ;

VILLASENOR, JA .

STATISTICS & PROBABILITY LETTERS, 1986, 4 (01) :47-49

[2]

Durrett R., 2019, PROBABILITY THEORY E, V49

[3] Generalized definition of the geometric mean of a non negative random variable [J].

Feng, Changyong ;

Wang, Hongyue ;

Zhang, Yun ;

Han, Yu ;

Liang, Yuefeng ;

Tu, Xin M. .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (07) :3614-3620

[4] Geometric Mean of Nonnegative Random Variable [J].

Feng, Changyong ;

Wang, Hongyue ;

Tu, Xin M. .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2013, 42 (15) :2714-2717

[5]

Royden H.L., 2018, Real analysis

[6]

Shao Jun., 2003, MATH STAT, DOI DOI 10.1007/B97553

[7]

Steele J.M., 2004, CAUCHY SCHWARZ MASTE

[8] The geometric mean? [J].

Vogel, Richard M. .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51 (01) :82-94

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