广义逆老化强度函数
On Generalized Reversed Aging Intensity Functions
摘要：
反向老化强度函数定义为瞬时反向风险率与反向风险率基线值的比值。定量分析了老化性能，反向老化强度越高，老化趋势越弱。本文引入并研究了一类广义逆老化强度函数。这些函数依赖于一个实参数。当参数为正时，它们唯一地刻画了一元正绝对连续随机变量的分布函数，在相反的情况下，它们刻画了分布族。进一步定义并研究了广义逆时效强度序。最后给出了几个数值例子。
英文摘要：
The reversed aging intensity function is defined as the ratio of the instantaneous reversed hazard rate to the baseline value of the reversed hazard rate. It analyzes the aging property quantitatively, the higher the reversed aging intensity, the weaker the tendency of aging. In this paper, a family of generalized reversed aging intensity functions is introduced and studied. Those functions depend on a real parameter. If the parameter is positive they characterize uniquely the distribution functions of univariate positive absolutely continuous random variables, in the opposite case they characterize families of distributions. Furthermore, the generalized reversed aging intensity orders are defined and studied. Finally, several numerical examples are given.
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