Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$, $a > 0$. As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

帕累托分布是极值理论中的一个重要分布。在本文中，我们考虑了具有 Pareto 分量的并行系统，并研究了异质性对此类系统偏度的影响。结果表明，当组件的寿命具有不同的形状参数时，具有异构Pareto组件寿命的并行系统比具有独立同分布Pareto组件的系统更偏斜。但是，对于组件的生命周期具有不同尺度参数的情况，结果在星形排序的意义上是相反的。我们还通过扩展 Deshpande 和 Kochar [(1983). 分散排序与尾排序相同。应用概率的进展15(3): 686–687] 从支持$(0, \infty )$到一般支持$(a, \infty )$ , $a > 0$。因此，我们从异构 Pareto 样本中获得了一些关于分散排序的顺序统计分散的新结果。