We show that the kth order statistic from a heterogeneous sample of n ≥ k exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan [14]. As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of Pǎltǎnea [11]. Extensions to general spacings are also presented.

中文翻译：

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异质指数样本阶数统计的随机比较

我们证明了ķ来自异质样本的 th 阶统计量n≥ķ正如 Xu 和 Balakrishnan [14] 所推测的那样，在星序的意义上，指数随机变量大于来自同质指数样本的随机变量。因此，我们为异质和同质指数样本之间的顺序统计建立了危险率排序，解决了 Pǎltǎnea [11] 的一个开放问题。还介绍了对一般间距的扩展。