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ON ORDERINGS BETWEEN WEIGHTED SUMS OF RANDOM VARIABLES

Published online by Cambridge University Press:  10 December 2012

Tiantian Mao ,
Xiaoqing Pan  and
Taizhong Hu
Tiantian Mao
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: mttiy@mail.ustc.edu.cn; panxq@mail.ustc.edu.cn; thu@ustc.edu.cn
Xiaoqing Pan
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: mttiy@mail.ustc.edu.cn; panxq@mail.ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China E-mail: mttiy@mail.ustc.edu.cn; panxq@mail.ustc.edu.cn; thu@ustc.edu.cn
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Abstract

Linear combinations of independent random variables have been extensively studied in the literature. Xu & Hu [21] and Pan, Xu, & Hu [16] unified the study of linear combinations of independent random variables under the general setup. This paper is a companion one of these two papers. In this paper, we will further study this topic. The results are further generalized to the cases of permutation invariant random variables and of independent but not necessarily identically distributed random variables which are ordered in the likelihood ratio or the hazard ratio order.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 85 - 97
Copyright
Copyright © Cambridge University Press 2013

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