Weighted (residual) varentropy with properties and applications

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.