Further results on closure properties of LPQE order

Di Crescenzo and Longobardi (2002) introduced the past entropy, Sunoj et al. (2013) gave a quantile version for the past entropy, termed as the past quantile entropy (PQE). Based on the PQE function, they defined a new stochastic order called as less PQE (LPQE) order and studied some properties of this order. In the present paper, we focus our interests on further closure properties of this new order. Some characterizations of the LPQE order are investigated, closure and reversed closure properties are obtained. The preservation of the LPQE order in the proportional failure rate and reversed failure rate models is discussed.