Some new results on the Rényi quantile entropy Ordering

Rényi (1961) proposed the Rényi entropy. Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Nanda et al. (2014) obtained a quantile version of the Rényi residual entropy, the Rényi residual quantile entropy (RRQE). Based on the RRQE function, they defined a new stochastic order, the Rényi quantile entropy (RQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the RQE order are investigated, closure and reversed closure properties are obtained, meanwhile, some illustrative examples are shown. As applications of a main result, the preservation of the RQE order in several stochastic models are discussed.