Generalized cumulative residual entropy for distributions with unrestricted supports

Authors:
Noomane Drissi;Thierry Chonavel;Jean Marc Boucher
Affiliations:
Lab-STICC (CNRS FRE), Institut Telecom, Telecom Bretagne, Technopole Brest Iroise, Brest Cédex, France;Lab-STICC (CNRS FRE), Institut Telecom, Telecom Bretagne, Technopole Brest Iroise, Brest Cédex, France;Lab-STICC (CNRS FRE), Institut Telecom, Telecom Bretagne, Technopole Brest Iroise, Brest Cédex, France
Venue:
Research Letters in Signal Processing
Year:
2008

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Abstract

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.