In actuarial science, it is often of interest to compare stochastically extreme claim amounts from heterogeneous portfolios. In this regard, in the present work, we compare the smallest order statistics arising from two heterogeneous portfolios in the sense of the usual stochastic, hazard rate, reversed hazard rate and likelihood ratio orderings. We also consider the multiple-outlier model and obtain some ordering results. It is assumed that the portfolios belong to the general exponentiated location-scale model. The results obtained here are based on vector majorization of parameters and multivariate chain majorization with heterogeneity in different parameters. For the purpose of illustration, the derived results are applied to some well known distributions. Various examples and counterexamples are also provided. Finally, a simulation study is conducted to validate some of the results established here.

在精算科学中，经常比较随机来自不同类别投资组合的极端索赔额是很有意义的。在这方面，在当前的工作中，我们从通常的随机性，风险率，逆向风险率和似然比排序的意义上比较了两个异构投资组合产生的最小订单统计量。我们还考虑了多离群模型并获得了一些排序结果。假设投资组合属于一般指数地点规模模型。此处获得的结果基于参数的向量主化和在不同参数中具有异质性的多元链主化。为了说明的目的，将得出的结果应用于一些众所周知的分布。还提供了各种示例和反示例。最后，