On Bounds for Moments of Unimodal Distributions

被引：0

作者：

Sharma, R. ^{[1
]}

Bhandari, R. ^{[1
]}

机构：

[1] Himachal Pradesh Univ, Dept Math & Stat, Shimla 171005, India

来源：

COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS | 2014年 / 21卷 / 03期

关键词：

Discrete distributions; harmonic mean; Kantorovich inequality; moments; unimodal distributions; variance;

D O I：

10.5351/CSAM.2014.21.3.201

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 provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

引用

页码：201 / 212

页数：12

共 13 条

[1] VARIANCE UPPER-BOUNDS AND CONVOLUTIONS OF ALPHA-UNIMODAL DISTRIBUTIONS [J].