Further Results on the DMRL Ordering

Let and be two nonnegative absolutely continuous random variables with respective distribution functions and such that , right-continuous inverse functions and , and survival functions and , respectively. We write , and say is smaller than in the DMRL (decreasing mean residual life) order, if the function is increasing in .
Some characterization properties of the DMRL order are investigated. The closure and reversed closure properties of the DMRL order are obtained. Meanwhile, some illustrative examples that meet the DMRL order are shown as well.