Sufficient conditions for some transform orders based on the quantile density ratio

Abstract

In this paper, we focus on providing sufficient conditions for some transform orders whenever the quantile densities ratio is non-monotone and, therefore, the convex transform order does not hold. These results have interest in comparing random variables with not explicit expression of their quantile functions and/or they are not easy to deal with. In addition, the main results are applied to compare two Tukey generalized distributed random variables and to establish new relationships among non-monotone and positive aging notions.