Di Crescenzo and Longobardi (J Appl Prob 39, 434–440, 2002), introduced the concept of past entropy for measuring uncertainty contained in past lifetime of random variables. By analogous to past entropy, Krishnan et al. (J Korean Stat Soc, 49, 457–474, 2020) defined the concept of past extropy. In this work, we propose nonparametric estimator for the past extropy, where the observations under consideration exhibit \(\alpha \)-mixing dependence. Asymptotic properties of the proposed estimator are derived under suitable regularity conditions. A Monte–Carlo simulation study is carried out to compare the performance of the estimators using the mean squared error.

Di Crescenzo和Longobardi（J Appl Prob 39，434–440，2002）引入了过去熵的概念，用于测量随机变量过去寿命中的不确定性。通过类似于过去的熵，克里希南等人。（J Korean Stat Soc，49，457–474，2020）定义了过去外向的概念。在这项工作中，我们为过去的外推提出非参数估计量，其中所考虑的观测值表现出\（\ alpha \） -混合依赖性。拟议估计量的渐近性质是在适当的规律性条件下得出的。进行了蒙特卡洛模拟研究，以使用均方误差比较估计器的性能。