  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.
