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Some Inequalities of Linear Combinations of Independent Random Variables. I.

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Maochao Xu  and
Taizhong Hu
Maochao Xu*
Affiliation:
Illinois State University
Taizhong Hu*
Affiliation:
University of Science and Technology of China
*
∗ Postal address: Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USA. Email address: mxu2@ilstu.edu
∗∗ Postal address: Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China. Email address: thu@ustc.edu.cn
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Abstract

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In this paper we provide some sufficient conditions to stochastically compare linear combinations of independent random variables. The main results extend those given in Proschan (1965), Ma (1998), Zhao et al. (2011), and Yu (2011). In particular, we propose a new sufficient condition to compare the peakedness of linear combinations of independent random variables which may have heavy-tailed properties.

Keywords

Likelihood ratio ordermajorizationpeakedness orderstochastic order

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 1179 - 1188
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

Supported by the NNSF of China (grant numbers 11071232 and 70821001) and the National Basic Research Program of China (973 Program, grant number 2007CB814901).

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