Generalized cumulative residual entropy and record values

Georgios Psarrakos () and Jorge Navarro ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 5, 623-640

Abstract: The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, 2004 ). The new concept called generalized cumulative residual entropy (GCRE) is related with the record values of a sequence of i.i.d. random variables and with the relevation transform. We also consider a dynamic GCRE obtained using the residual lifetime. For these concepts we obtain some characterization results, stochastic ordering and aging classes properties and some relationships with other entropy concepts. Copyright Springer-Verlag 2013

Keywords: Generalized cumulative residual entropy; Failure (hazard) rate; Record values; Nonhomogeneous Poisson process; Mean residual waiting time (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (22)

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DOI: 10.1007/s00184-012-0408-6

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