Stochastic comparisons of finite mixtures with general exponentiated location-scale distributed components

In this paper, we study stochastic ordering results between two finite mixtures with single and multiple outliers, assuming subpopulations follow general exponentiated location-scale distributions. For single-outlier mixtures, several sufficient conditions are derived under which the mixture variables are ordered in the usual stochastic, reversed hazard rate, and likelihood ratio orders, using majorization concepts. For multiple-outlier mixtures, results are obtained for the reversed hazard rate, likelihood ratio, and ageing faster orders in reversed hazard rate. Numerical examples and counterexamples are presented to illustrate and support the established theoretical findings.