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On weighted residual and past entropies. (English) Zbl 1106.62114
Summary: We consider a “length-biased” shift-dependent information measure related to the differential entropy, in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of “weighted residual entropy” and “weighted past entropy”, that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced by N. Ebrahimi [J. Stat. Plann. Inference 64, No. 1, 9–19 (1997; Zbl 0904.62056); Sankhyā, Ser. A 58, No. 1, 48–56 (1996; Zbl 0893.62098)]. The obtained results include their behaviors under monotonic transformations.

MSC:
62N05 Reliability and life testing
62B10 Statistical aspects of information-theoretic topics
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