Ordering results of extreme order statistics from multiple-outlier scale models with dependence

TL;DR

This paper investigates how the largest and smallest extreme order statistics compare under multiple-outlier scale models with dependence, using Archimedean copulas to model the dependence structure.

Contribution

It provides new sufficient conditions for stochastic comparisons of extreme order statistics in dependent multiple-outlier scale models.

Findings

Established conditions for stochastic ordering of largest order statistics.

Compared smallest order statistics using various stochastic orders.

Illustrated theoretical results with concrete examples.

Abstract

In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables. Sufficient conditions are obtained for comparison of the largest order statistics in the sense of the usual stochastic, reversed hazard rate, star and Lorenz orders. The smallest order statistics are also compared with respect to the usual stochastic, hazard rate, star and Lorenz orders. To illustrate the theoretical establishments, some examples are provided.