HR and RHR orderings of generalized order statistics

In this article, we compare generalized order statistics in terms of increasing convex, mean residual life, hazard rate and reversed hazard rate orderings and establish some general results, including resolving an open problem. Some counterexamples are also provided for the cases wherein the results are not valid in general. Finally, some new applications of these results are demonstrated for sequential systems, k-record values and Pfeifer’s records.