Article ID Journal Published Year Pages File Type
1151834 Statistics & Probability Letters 2013 4 Pages PDF
Abstract

Let X1,…,XnX1,…,Xn (Y1,…,YnY1,…,Yn) be independent random variables such that XiXi (YiYi) follows the gamma distribution with shape parameter αα and mean αλi(αμi), α>0,λi>0α>0,λi>0 (μi>0μi>0), i=1,…,ni=1,…,n. Let λ=(λ1,…,λn), μ=(μ1,…,μn) and let r̃n:n(λ;x) (r̃n:n(μ;x)) denote the reversed hazard rate of max{X1,…,Xn}max{X1,…,Xn} (max{Y1,…,Yn}max{Y1,…,Yn}). In this note we show that if λ weakly majorizes μ then r̃n:n(λ;x)≥r̃n:n(μ;x),∀x>0, thereby strengthening the results of Dykstra et al. (1997), and Lihong and Xinsheng (2005).

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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