The reversed hazard rate function
The reversed hazard rate function
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DOI：
10.1017/s0269964800005064
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发表时间：
1998-01-01
影响因子：
1.1
通讯作者：
Singh, H
中科院分区：
文献类型：
--
作者：
Block, HW;Savits, TH;Singh, H
在本文中，我们讨论了逆风险率函数的一些性质。该函数已被证明在存在左删失观察的数据分析中非常有用。用相反的时间尺度来讨论生命周期也是很自然的。事实上，普通的危险率函数对于生命周期来说是最有用的，如果时间尺度逆转，则反向危险率是自然的。混淆这些概念通常（尽管并非总是）会导致异常情况。例如，一个结果表明，如果逆风险率函数正在增加，则其支持区间必须为 (-无穷大,b)，其中 b 是有限的。因此，非负随机变量不能增加反向风险率。由于这一结果，文献中有关反向危险率排序的一些现有结果需要修改。反向危险率在系统研究中也很重要。危险率与系列系统有密切关系；反向危险率似乎更适合研究并行系统。给出的几个结果证明了这一点。在研究系统时，一个问题是将系统的危险率函数和逆危险率函数的导数与组件的相似量相关联。我们给出了一些解决这个问题的结果。最后，我们对 n 个系统中的 k 个系统进行逆向风险率排序的比较。
In this paper we discuss some properties of the reversed hazard rate function. This function has been shown to be useful in the analysis of data in the presence of left censored observations. It is also natural in discussing lifetimes with reversed time scale. In fact, ordinary hazard rate functions are most useful for lifetimes, and reverse hazard rates are natural if the time scale is reversed. Mixing up these concepts can often, although not always, lead to anomalies. For example, one result gives that if the reversed hazard rate function is increasing, its interval of support must be (-infinity,b) where b is finite. Consequently nonnegative random variables cannot have increasing reversed hazard rates. Because of this result some existing results in the literature on the reversed hazard rate ordering require modification.Reversed hazard rates are also important in the study of systems. Hazard rates have an affinity to series systems; reversed hazard rates seem more appropriate for studying parallel systems. Several results are given that demonstrate this. In studying systems, one problem is to relate derivatives of hazard rate functions and reversed hazard rate functions of systems to similar quantities for components. We give some results that address this. Finally, we carry out comparisons for k-out-of-n systems with respect to the reversed hazard rate ordering.