Some new stochastic orders based on quantile function

Recently, in the literature, the use of quantile functions in the place of distribution functions has provided new models, alternative methodology and easier algebraic manipulations. In this paper, we introduce new orders among the random variables in terms of their quantile functions like the reversed hazard quantile function, the reversed mean residual quantile function and the reversed variance residual quantile function orders. The relationships among the proposed orders and some existing orders are also discussed.