In information theory, it is of recent interest to study variability of uncertainty measure. 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 effect under monotonic transformations, bounds are investigated. Further, we study weighted varentropy for coherent systems and weighted residual varentropy for proportional hazard rate models. Finally, applications of the weighted residual varentropy are discussed for some distributions.

翻译：在信息论中，不确定性度量的变异性研究是近期关注的焦点。为此，近年来多位学者引入了变熵的概念并进行了研究。本文探讨了加权的变熵和加权的残余变熵，研究了这些变异性度量在单调变换下的效应、界限等若干理论性质。进一步，我们针对相干系统研究了加权的变熵，并针对比例风险率模型研究了加权的残余变熵。最后，讨论了加权的残余变熵在某些分布中的应用。