In this article, we give several results on (multivariate and
univariate) stochastic comparisons of generalized order statistics. We
give conditions on the underlying distributions and the parameters on
which the generalized order statistics are based, to obtain stochastic
comparisons in the stochastic, dispersive, hazard rate, and likelihood
ratio orders. Our results generalize some recent results for order
statistics, record values, and generalized order statistics and provide
some new results for other models such as k-record values and
order statistics under multivariate imperfect repair.