递减剩余Extropy (DRE)年龄性质是最近新提出的一个概念, 其在可靠性理论中的意义表示元件年龄的不确定性随使用时间递减. 文章研究如何检 验随机变量是否是DRE的问题. 首先定义了一个随机序比较DRE 性质的强弱, 并依此序导出一个度量DRE性质的参数. 之后利用核密度估计的相关知识构造了一个渐近无偏的$U$统计量来估计该参数, 该检验统计量的值过大时接受随机变量是DRE 的假设. 在一定条件下证明了检验统计量的渐近正态性, 从而得到检验的渐近临界值. 最后确定了核密度估计的最优形式, 并进行了数值模拟.

The decresing residual extropy (DRE) aging property was presented most recently. The significance of DRE aging property in reliability is that the uncertainty of one component is decresing during use. The main topic of this paper is how to test whether one random variable is DRE or not. First of all, we define a stochastic order to compare the strength of DRE property between two random variables. Based on this point, a parameter is derived to measure the DRE property. With the help of the related knowledge of kernel density estimation, we construct an asymptotic unbiased $U$-statistic to estimate the parameter. We accept the DRE hypothesis when the test statistic is too large. To get the asymptotic critical value of the test, the asymptotic normality of the asymptotic unbiased $U$-statistic is proved. Finally, we derive the optimal form of the kernel density estimation, and proceed the numerical simulation.