In this paper, we consider Marshall and Olkin’s family of distributions. The parent (baseline) distribution is taken to be a scaled family of distributions. Two models: (i) modified proportional hazard rate scale and (ii) modified proportional reversed hazard rate scale, are considered. Some stochastic comparison results in terms of the usual stochastic, hazard rate and reversed hazard rate orders are studied to compare order statistics formed from two sets of independent observations following these models. Most of the sufficient conditions are obtained depending on various majorization-type partial orderings. Further, the setup with multiple-outlier model is taken. Various stochastic orders between the smallest and largest order statistics are developed. Several numerical examples are provided to illustrate the effectiveness of the established theoretical results.

在本文中，我们考虑了马歇尔和奥尔金的分布族。父（基线）分布被视为比例分布族。考虑了两个模型：（i）修正的比例危险率量表和（ii）修正的比例逆向危险率量表。研究了一些随机比较结果，这些随机比较结果是按照通常的随机，危险率和逆向危险率顺序进行的，以比较由遵循这些模型的两组独立观测值形成的顺序统计量。取决于各种主要化类型的局部排序，可以获得大多数的充分条件。此外，采用具有多个异常值模型的设置。最小和最大订单统计之间的各种随机订单被开发出来。