On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components

Neeraj Misra and Amit Kumar Misra

Statistics & Probability Letters, 2013, vol. 83, issue 6, 1567-1570

Abstract: Let X1,…,Xn (Y1,…,Yn) be independent random variables such that Xi (Yi) follows the gamma distribution with shape parameter α and mean αλi(αμi), α>0,λi>0 (μi>0), i=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{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: Gamma distribution; Hazard rate order; Majorization; Reversed hazard rate order; Usual stochastic order (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spl.2013.03.002

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