Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1151834 | Statistics & Probability Letters | 2013 | 4 Pages |
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).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Neeraj Misra, Amit Kumar Misra,