Generalized cumulative residual entropy and record values |
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Authors: | Georgios Psarrakos Jorge Navarro |
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Affiliation: | 1. Department of Statistics and Insurance Science, University of Piraeus, Athens, Greece 2. Facultad de Matemáticas, Universidad de Murcia, 30100, ?Murcia, Spain
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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. |
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