This paper deals with stochastic comparisons of the largest order statistics arising from two sets of independent and heterogeneous gamma samples. It is shown that the weak supermajorization order between the vectors of scale parameters together with the weak submajorization order between the vectors of shape parameters imply the reversed hazard rate ordering between the corresponding maximum order statistics. We also establish sufficient conditions of the usual stochastic ordering in terms of the p-larger order between the vectors of scale parameters and the weak submajorization order between the vectors of shape parameters. Numerical examples and applications in auction theory and reliability engineering are provided to illustrate these results.

中文翻译：

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来自异构 Gamma 样本的最大阶统计的比较

本文处理由两组独立和异质伽马样本产生的最大阶统计的随机比较。结果表明，尺度参数向量之间的弱超主要化顺序以及形状参数向量之间的弱次主要化顺序意味着相应的最大阶统计量之间的危险率顺序相反。我们还建立了通常随机排序的充分条件p- 尺度参数向量之间的大阶和形状参数向量之间的弱次优阶。提供了拍卖理论和可靠性工程中的数值例子和应用来说明这些结果。