In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study the weighted varentropy and weighted residual varentropy. Several theoretical results of these variability measures such as the effect under monotonic transformations and bounds are investigated. Importance of the weighted residual varentropy over the residual varentropy is presented. Further, we study weighted varentropy for coherent systems and weighted residual varentropy for proportional hazard rate models. A kernel-based non-parametric estimator for the weighted residual varentropy is also proposed. The estimation method is illustrated using simulated and two real data sets.

翻译：在信息论中，研究不确定性度量的变异性是近年来的一个热点。为此，变熵的概念最近已被多位学者提出并研究。本文中，我们研究了加权变熵与加权残差变熵。我们探讨了这些变异性度量的若干理论性质，例如单调变换下的影响及其界。文中阐述了加权残差变熵相较于残差变熵的重要性。进一步，我们研究了相干系统的加权变熵以及比例风险率模型的加权残差变熵。此外，我们还提出了一种基于核的非参数估计器用于估计加权残差变熵。该估计方法通过模拟数据和两个真实数据集进行了验证。