Weighted Renyi's entropy for lifetime distributions

Recently, Di Crescenzo and Longobardi (2006 Di Crescenzo, A., Longobardi, M. (2006). On weighted residual and past entropies. Sci. Math. Jpn. 64:255–266. Google Scholar]) have studied “length-biased” shift-dependent information measure and its dynamic versions. On the other hand, Renyi's entropy plays a vital role in the literature of information theory that is a generalization of Shannon's entropy. In this article, the concepts of weighted Renyi's entropy, weighted residual Renyi's entropy, and weighted past Renyi's entropy are introduced and their properties are discussed.