Right Spread Order of the Second-Order Statistic from Heterogeneous Exponential Random Variables
Right Spread Order of the Second-Order Statistic from Heterogeneous Exponential Random Variables
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DOI：
10.1080/03610926.2010.493277
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
P. Zhao;Xiaohu Li;Gaofeng Da
中科院分区：
文献类型：
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作者：
P. Zhao;Xiaohu Li;Gaofeng Da
设X1，.，Xn为独立指数随机变量，其各自的危险率为λ1，.，λ n，Y1，.，Yn为独立同分布。具有共同风险率λ的指数随机变量。证明了X1，...，Xn的二阶统计量X2：n大于Y1，...，Yn的二阶统计量Y2：n，当且仅当且且当Λ i = Λ（1）-λ i，且X2：n小于Y2：n关于右扩散阶的充要条件进一步研究了风险率成比例递减的情形，所得结果是文献中一些相应结果的很好推广.
Let X 1,…, X n be independent exponential random variables with respective hazard rates λ1,…, λ n , and Y 1,…, Y n be i.i.d. exponential random variables with common hazard rate λ. It is proved that X 2: n , the second order statistic from X 1,…, X n , is larger than Y 2: n , the second order statistic from Y 1,…, Y n , with respect to the right spread order if and only if with and Λ i = Λ(1) − λ i , and X 2: n is smaller than Y 2: n with respect to the right spread order if and only if Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature.