On Weighted Residual and Past Entropies

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.

13 pages; updated on June 21, 2011

Cited by in corpus (3)

• Analysis and applications of the residual varentropy of random lifetimes
• On weighted cumulative residual extropy and weighted negative cumulative extropy
• General weighted cumulative residual (past) extropy of minimum (maximum) ranked set sampling with unequal samples