  We introduce two uncertainty measures, say weighted past varentropy (WPVE)
and weighted paired dynamic varentropy (WPDVE). Several properties have been
studied for these proposed measures. The effect of the monotone transformation
for these measures have been discussed. We have obtained an upper bound of the
WPVE using the weighted past Shannon entropy. A lower bound of the WPVE is also
obtained. The WPVE has been studied for proportional reversed hazard rate
(PRHR) models. Upper and lower bounds of the WPDVE have been derived. We
propose non-parametric kernel estimates of the WPVE and WPDVE. Further, maximum
likelihood estimation has been employed to estimate WPVE and WPDVE for an
exponential population. A numerical simulation is provided to observe the
behaviour of the proposed estimates. Finally, we have analysed a real data set
and obtain the estimated values of WPVE.
