Some new results on the LQE ordering

Abstract

Ebrahimi and Pellerey (1995) and Ebrahimi (1996) proposed the residual entropy. Recently, Sunoj and Sankaran (2012) obtained a quantile version of the residual entropy, the residual quantile entropy (RQE). Based on the RQE function, they defined a new stochastic order, the less quantile entropy (LQE) order, and studied some properties of this order. In this paper, we focus on further properties of this new order. Some characterizations of the LQE 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 LQE order in several stochastic models is discussed. We give the closure and reversed closure properties of the LQE order for coherent systems with dependent and identically distributed components, and also consider a potential application to insurance of this order.