Some preservation properties of shifted stochastic orders

In this paper, we provide results on preservation of various shifted stochastic orders under the operations of mixtures. These results have been established with respect to up (down) shifted hazard rate order, up (down) shifted reversed hazard rate order and up (down) shifted likelihood ratio order. In addition, a discussion on preservation of shifted stochastic orders under the operations of convolutions is also presented. Some examples have been obtained to illustrate applications of these results. © Brazilian Statistical Association, 2021