Stochastic comparison results between two finite mixture models with generalized Marshall-Olkin Topp Leone G distributed components

Finite mixture models (FMMs) are widely applied in reliability engineering to characterize the lifetime distributions of heterogeneous populations. This paper establishes stochastic comparison results for two FMMs whose component distributions belong to the generalized Marshall–Olkin Topp Leone-G (MOTL-G) family, which uses a scale family as the baseline distribution. The analysis is conducted within the framework of majorization, chain majorization, and unordered majorization orders. We first derive sufficient conditions under which the usual stochastic order and the hazard rate order hold between two FMMs, in terms of majorization and chain majorization orders applied to the shape, scale, and mixing proportion parameters. Subsequently, we develop sufficient conditions based on unordered majorization orders for the usual stochastic order between two FMMs. Using aluminum alloy fatigue life data, we validate the flexibility of the proposed model and successfully identify its underlying heterogeneous structure. The theoretical findings are illustrated and validated through numerical examples and counterexamples.