Usual Multivariate Stochastic Order on the Proportional Reversed Hazard Rates Model

Let , , , be all independent PRHR variables. Firstly, we show that implies . Secondly, we consider the comparison of convolutions of independent heterogeneous PRHR variables with respect to the usual stochastic ordering. Suppose and , we prove that implies , for all . The results established here strengthen some of the results known in the literature.