On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

TL;DR

This paper investigates the stochastic ordering of second-order statistics from two batches of exponentiated location-scale distributed variables, providing conditions for stochastic and hazard rate orders and illustrating applications.

Contribution

It introduces new sufficient conditions for stochastic and hazard rate ordering of second-order statistics in exponentiated location-scale models, extending existing theoretical frameworks.

Findings

Derived conditions for stochastic orderings of second-order statistics.

Established hazard rate order conditions for these distributions.

Presented applications demonstrating the theoretical results.

Abstract

Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of parameters is switched to another vector of parameters in the specified model. Sufficient conditions for the usual stochastic order and the hazard rate order are derived. Some applications of the established results are presented.