Ordering properties of sample minimum from Kumaraswamy-G random variables

TL;DR

This paper investigates the ordering properties of sample minimums from Kumaraswamy-G distributed variables, establishing stochastic and hazard rate orderings under various conditions, including likelihood ratio ordering for outlier samples.

Contribution

It introduces new ordering results for minimums of Kumaraswamy-G samples, especially for heterogeneous and outlier cases, expanding understanding of their stochastic behavior.

Findings

Established stochastic and hazard rate orderings for Kumaraswamy-G minimums.

Proved likelihood ratio ordering for outlier heterogeneous samples.

Compared minimums across different parent distributions.

Abstract

In this paper we compare the minimums of two independent and heterogeneous samples each following Kumaraswamy-G distribution with the same and the different parent distribution functions. The comparisons are carried out with respect to usual stochastic ordering and hazard rate ordering with majorized shape parameters of the distributions. The likelihood ratio ordering between the minimum order statistics is established for heterogeneous multiple outlier Kumaraswamy-G random variables with the same parent distribution function