Stochastic comparisons of finite mixture models derived from distorted distributions: results based on vector and multivariate chain majorization approaches

In this paper, we focus on classical finite mixture models, which are widely used in modeling lifetime distributions for random samples arising from heterogeneous populations. We then develop results in two directions. First, we carry out stochastic comparisons of finite mixture models derived from distorted distributions based on vector majorization. Next, we use the concept of multivariate chain majorization to establish further comparison results for finite mixture models from distorted distributions. These comparisons are made in terms of various stochastic orders, including the usual stochastic, hazard rate, reversed hazard rate and dispersive orders.