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Research Letters in Signal Processing
Volume 2008 (2008), Article ID 790607, 5 pages
Research Letter

Generalized Cumulative Residual Entropy for Distributions with Unrestricted Supports

Lab-STICC (CNRS FRE 3167), Institut Telecom, Telecom Bretagne, Technopole Brest Iroise, CS 83818, 29238 Brest CĂ©dex, France

Received 6 April 2008; Accepted 19 June 2008

Academic Editor: Andreas Jakobsson

Copyright © 2008 Noomane Drissi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the cumulative residual entropy (CRE) a recently introduced measure of entropy. While in previous works distributions with positive support are considered, we generalize the definition of CRE to the case of distributions with general support. We show that several interesting properties of the earlier CRE remain valid and supply further properties and insight to problems such as maximum CRE power moment problems. In addition, we show that this generalized CRE can be used as an alternative to differential entropy to derive information-based optimization criteria for system identification purpose.