ON PARALLEL SYSTEMS WITH HETEROGENEOUS GAMMA COMPONENTS
ON PARALLEL SYSTEMS WITH HETEROGENEOUS GAMMA COMPONENTS
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DOI：
10.1017/s0269964811000064
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发表时间：
2011-05
影响因子：
1.1
通讯作者：
P. Zhao
中科院分区：
文献类型：
--
作者：
P. Zhao
本文从似然比阶和危险率阶的角度研究了具有两个独立非均质伽马分量的并联系统寿命的有序性质。设X1和X2是两个独立的随机变量，其中Xi具有形状参数r>和尺度参数λi， i= 1,2，设X*1和X*2是另一组独立的随机变量，其中X*i具有形状参数r和尺度参数λ*i， i= 1,2。分别用X2:2和X*2:2表示相应的最大阶统计量。证明了其中，如果（λ1, λ2）弱多数化（λ*1, λ*2），则X2:2在似然比序意义上随机大于X*2:2。另外，我们还证明了如果0<r≤1且（λ1, λ2） p大于（λ*1, λ*2），则X2:2在风险率顺序意义上随机大于X*2:2。这里得出的结果加强和推广了文献中已知的一些结果。
In this article, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous gamma components in terms of the likelihood ratio order and the hazard rate order. Let X1 and X2 be two independent gamma random variables with Xi having shape parameter r>0 and scale parameter λi, i=1, 2, and let X*1 and X*2 be another set of independent gamma random variables with X*i having shape parameter r and scale parameter λ*i, i=1, 2. Denote by X2:2 and X*2:2 the corresponding maximum order statistics, respectively. It is proved that, among others, if (λ1, λ2) weakly majorize (λ*1, λ*2), then X2:2 is stochastically greater than X*2:2 in the sense of likelihood ratio order. We also establish, among others, that if 0<r≤1 and (λ1, λ2) is p-larger than (λ*1, λ*2), then X2:2 is stochastically greater than X*2:2 in the sense of hazard rate order. The results derived here strengthen and generalize some of the results known in the literature.