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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Acknowledgments
JN is partially supported by Ministerio de Ciencia y Tecnología and Fundación Séneca under grants MTM2009-08311 and 08627/PI/08.
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Psarrakos, G., Navarro, J. Generalized cumulative residual entropy and record values. Metrika 76, 623–640 (2013). https://doi.org/10.1007/s00184-012-0408-6
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DOI: https://doi.org/10.1007/s00184-012-0408-6