On upper bounds for the variance of functions of random variables with weighted distributions

被引：2
|
作者：
Goodarzi F. [1 ]
Amini M. [1 ]
Mohtashami Borzadaran G.R. [1 ]
机构：
[1] Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad
来源：
Lobachevskii Journal of Mathematics | 2016年 / 37卷 / 4期
关键词：
Chernoff inequality; increasing failure rate; log-concave; size-biased distribution; Variance bounds;
D O I：
10.1134/S1995080216040089
中图分类号：
学科分类号：
摘要：
Cacoullos and Papathanasiou (1989) obtained a characterization for the distribution of a random variable via the upper bounds for the variance of a given function of that random variable. In this paper, on the basis of their works, we derive a characterization for the weighted distribution. Subsequently, by using the characterization and in terms of Chernoff-type inequalities, we find the upper bounds for the variance of a given function of the weighted random variable. Moreover, assuming that X is IFR [increasing failure rate] we compute an upper bound for the variance of this function. © 2016, Pleiades Publishing, Ltd.
引用
收藏
页码：422 / 435
页数：13
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