On multivariate orderings of some general ordered random vectors

TL;DR

This paper introduces new models, DSOS and DGOS, that better capture dependency structures in ordered random vectors, extending existing models like GOS and SOS, and analyzes their properties under Archimedean copulas.

Contribution

It develops the DSOS and DGOS models to describe dependency structures in ordered random vectors, expanding the theoretical framework beyond GOS and SOS.

Findings

DSOS and DGOS models effectively describe dependency structures.

Univariate and multivariate ordering properties are established.

Results apply to both one-sample and two-sample scenarios.

Abstract

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.