# Ordering properties of the smallest order statistic from Weibull G random variables

## TL;DR

This paper investigates the ordering properties of the smallest order statistic from Weibull-G distributed samples across three different scenarios, considering independence, random shocks, and dependence via copulas.

## Contribution

It introduces a comprehensive comparison framework for the minimums of Weibull-G samples under various dependence structures and shock conditions.

## Key findings

- Orderings established under vector majorization
- Results extend to dependent structures with Archimedean copulas
- Comparison results hold for heterogeneous Weibull-G samples

## Abstract

In this paper we compare the minimums of two heterogeneous samples each following Weibull-G distribution under three scenarios. In the Fifirst scenario, the units of the samples are assumed to be independently distributed and the comparisons are carried out through vector majorization. The minimums of the samples are compared in the second scenario when the independent units of the samples also experience random shocks. The last scenario describes the comparison when the units have a dependent structure sharing Archimedean copula.