On Weighted Residual and Past Entropies

By A. Di Crescenzo, M. Longobardi. 2006

129 citations recorded by the source corpus.

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.

Subfields: Demography, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/69176e6fc738fbcc0e093652f06c43752421a4a8

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Citations in the corpus

On weighted extropies (2020, methodology): “, a random variable X has the same Shannon entropy of Xþ b, for any b 2 R: To avoid this problem, the concept of weighted entropy has been introduced (see Di Crescenzo and Longobardi (2006)) as HwðXÞ 1⁄4 E X log f ðXÞ 1⁄4 ðþ1”
On weighted cumulative residual entropy (2017, background): “…the occurrence of the eventX = x that yields a “length-biased” shift dependent informationmeasure assigning greater importance to larger values of X. Di Crescenzo and Longobardi (2006) introduced the notions of “weighted residual entropy” and “weighted past entropy,” which are suitable to…”
Quantile based entropy function in past lifetime (2013, unknown): “For recent works on entropy in past lifetime we refer to Di Crescenzo and Longobardi (2002, 2006), Nanda and Paul (2006) and Kundu et al. (2010).”