Dispersive and star ordering of sample extremes from dependent random variables following the proportional odds model

TL;DR

This paper investigates how dispersive and star orders can be used to compare the variability and skewness of extreme values from dependent random variables modeled with the proportional odds model and Archimedean copula.

Contribution

It introduces new results on the ordering of extreme order statistics under dependence using dispersive and star orders within the PO model framework.

Findings

Dispersive order of sample extremes is characterized under dependence.

Star order comparisons reveal skewness differences in extremes.

Numerical examples illustrate the theoretical results.

Abstract

Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order statistics from dependent random variables following the proportional odds (PO) model. The joint distribution of the random variables is modeled with Archimedean copula. Numerical examples are provided to illustrate the findings.