On multivariate orderings of some general ordered random vectors

Ordered random vectors are frequently encountered in many problems. The generalized order statistics (GOSs) and sequential order statistics (SOSs) are two general models for ordered random vectors. However, these two models do not capture the dependency structures that may be present in the underlying random variables. In this paper, we study the developed sequential order statistics (D-SOSs) and developed generalized order statistics (D-GOSs) models that incorporate dependency structures among ordered random vectors. We then study various univariate and multivariate ordering properties of D-SOS and D-GOS models under Archimedean copula. We develop corresponding results for both one-sample and two-sample situations. We also present some simulational results and a real data analysis for illustrative purpose.