Stochastic Comparisons of Largest Order Statistics From Multiple-Outlier Exponential Models

In this paper, we carry out stochastic comparisons of largest order statistics from multiple-outlier exponential models according to the likelihood ratio order (reversed hazard rate order) and the hazard rate order (usual stochastic order). It is proved, among others, that the weak majorization order between the two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between largest order statistics, and that the p -larger order between the two hazard rate vectors is equivalent to the hazard rate order (usual stochastic order) between largest order statistics. We also extend these results to the proportional hazard rate models. The results established here strengthen and generalize some of the results known in the literature.