We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum) of one system dominates the other in hazard rate (reversed hazard rate) order. Further, we prove variation diminishing property (Karlin [8]) for all possible restrictions to derive the new results.

翻译：本文提出关于随机数目非同分布随机变量的最小值或最大值次序统计量比较的新结果。在非同分布设定下，我们证明在特定条件下，一个系统的随机最小值（最大值）在风险率（逆风险率）序意义下优于另一个系统。进一步，我们通过证明变差缩减性质（Karlin [8]）对所有可能的约束均成立，从而推导出这些新结果。