In this paper we focus on the study of the monotonicity properties of the residual and the past extropy as well as on some characterization problems. We then apply the derived results to analyze further stochastic aspects of order statistics, coherent systems, and record values. Using various examples, we illustrate the applicability and significance of the results obtained. In addition, non-parametric estimators for the residual and past extropy measures are introduced. The performance of the acquired estimators has been illustrated using simulated data sets and also real data sets.

翻译：本文重点研究残差熵与历史熵的单调性性质以及若干刻画问题。随后将所得结果应用于分析次序统计量、关联系统及记录值的进一步随机性质。通过多种示例，我们阐明了所得结果的适用性与重要性。此外，本文提出了残差熵与历史熵度量的非参数估计量，并基于模拟数据集与真实数据集展示了所获估计量的性能表现。