Concentration of the Ratio between the Geometric and Arithmetic Means

被引：12

作者：

Aldaz, J. M. ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2010年 / 23卷 / 02期

关键词：

Concentration of measure; Arithmetic mean; Geometric mean;

D O I：

10.1007/s10959-009-0215-9

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 explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights, one does obtain concentration around a value that depends on the sequence.

引用

页码：498 / 508

页数：11

共 50 条

[31] Arithmetic-geometric means revisited
Borwein, JM
Lisonek, P
Macdonald, JA
MAPLETECH, 1997, 4 (01): : 20 - 27
[32] ALGORITHMS INVOLVING ARITHMETIC AND GEOMETRIC MEANS
CARLSON, BC
AMERICAN MATHEMATICAL MONTHLY, 1971, 78 (05): : 496 - &
[33] Comparison of Arithmetic, Geometric, and Harmonic Means
Rozovsky, L. V.
MATHEMATICAL NOTES, 2021, 110 (1-2) : 118 - 125
[34] VARIANCE AND THE INEQUALITY OF ARITHMETIC AND GEOMETRIC MEANS
Rodin, Burt
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2017, 47 (02) : 637 - 648
[35] NOTE ON THE INEQUALITY OF THE ARITHMETIC AND GEOMETRIC MEANS
HAO, ZC
PACIFIC JOURNAL OF MATHEMATICS, 1990, 143 (01) : 43 - 46
[36] ARITHMETIC GEOMETRIC MEANS OF POSITIVE MATRICES
COHEN, JE
NUSSBAUM, RD
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1987, 101 : 209 - 219
[37] The theory of the arithmetic-geometric means
Geppert, H
MATHEMATISCHE ANNALEN, 1928, 99 : 162 - 180
[38] Relation between geometric-arithmetic and arithmetic-geometric indices
Gutman, Ivan
JOURNAL OF MATHEMATICAL CHEMISTRY, 2021, 59 (06) : 1520 - 1525
[39] On some mappings associated with geometric and arithmetic means
Dragomir, SS
Comanescu, D
Pearce, CEM
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1997, 55 (02) : 299 - 309
[40] Three inequalities for the arithmetic, identric, and geometric means
Seiffert, HJ
SIAM REVIEW, 1997, 39 (02) : 330 - 332

← 1 2 3 4 5 →