Characterizations based on generalized cumulative residual entropy functions

Jorge Navarro and Georgios Psarrakos

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1247-1260

Abstract: The Shannon entropy and the cumulative residual entropy (CRE) of a random variable are useful tools in probability theory. Recently, a new concept called generalized cumulative residual entropy (GCRE) of order n was introduced and studied. It is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. In this paper, we show that, under some assumptions, the GCRE function of a fixed order n uniquely determines the distribution function. Some characterizations of particular probability models are obtained from this general result.

Date: 2017
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DOI: 10.1080/03610926.2015.1014111

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