Ordered random vectors are frequently encountered in many problems. The generalized order statistics (GOS) and sequential order statistics (SOS) are two general models for ordered random vectors. However, these two models do not capture the dependency structures that are present in the underlying random variables. In this paper, we study the developed sequential order statistics (DSOS) and developed generalized order statistics (DGOS) models that describe the dependency structures of ordered random vectors. We then study various univariate and multivariate ordering properties of DSOS and DGOS models under Archimedean copula. We consider both one-sample and two-sample scenarios and develop corresponding results.

翻译：有序随机向量在诸多问题中频繁出现。广义次序统计量（GOS）和序列次序统计量（SOS）是有序随机向量的两个通用模型。然而，这两种模型未能捕捉底层随机变量中存在的相依结构。本文研究了用于描述有序随机向量相依结构的改进型序列次序统计量（DSOS）和改进型广义次序统计量（DGOS）模型。随后，我们在阿基米德Copula下探究了DSOS和DGOS模型的各类单变量及多元排序性质。我们同时考虑了单样本和双样本情景，并推导出相应结论。