A monotonicity property of variances

被引：4
|
作者：
Aldaz, J. M. [1 ]
机构：
[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
来源：
STATISTICS & PROBABILITY LETTERS | 2013年 / 83卷 / 05期
关键词：
Variance; Arithmetic-geometric inequality; GEOMETRIC MEANS; INEQUALITY;
D O I：
10.1016/j.spl.2013.02.004
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 prove that variances of non-negative random variables have the following monotonicity property: For all 0 < r < s <= 1, and all 0 <= X is an element of L-2, we have Var(X-r)(1/r) <= Var(X-s)(1/s). We also discuss the real valued case. (C) 2013 Elsevier B.V. All rights reserved.
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页码：1416 / 1419
页数：4
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