Probability in the Engineering and Informational Sciences

Table of Contents - July 2012 - Volume 26, Issue 03  

Research Article

SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

Subhash Kochara1 and Maochao Xua2

a1 Department of Mathematics and Statistics, Portland State University, Portland, OR

a2 Department of Mathematics, Illinois State University, Normal, IL E-mail: mxu2@ilstu.edu

Abstract

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].