Abstract
We consider a “length-biased” shift-dependent information measure, related
to the differential entropy in which higher weight is assigned to large values
of observed random variables. This allows us to introduce the notions of “weighted
residual entropy” and “weighted past entropy”, that are suitable to describe dynamic
information of random lifetimes, in analogy with the entropies of residual and past
lifetimes introduced in [9] and [6], respectively. The obtained results include their
behaviors under monotonic transformations.
