This study deals with random variables from gamma samples. For independent samples, it is found that when all the shape parameters are not smaller than 1, a less weakly supermajorized shape parameter vector implies a larger sample minimum in the sense of the hazard rate order. When the shape parameters are the same, a less weakly submajorized scale parameter vector also leads to a larger sample minimum in the sense of the hazard rate order. As for samples having FGM copula or FGM survival copula, a less majorized shape parameter vector results in a smaller sample maximum and a larger sample minimum with respect to the usual stochastic order. Several numerical examples and one application are provided to illustrate the theoretical findings.

中文翻译：

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来自独立或相关伽马样本的样本极值的随机比较

本研究处理来自伽马样本的随机变量。对于独立样本，发现当所有形状参数不小于 1 时，较弱的超大化形状参数向量意味着在危险率顺序意义上更大的样本最小值。当形状参数相同时，较弱的次大化尺度参数向量也导致在危险率顺序意义上更大的样本最小值。对于具有 FGM copula 或 FGM 生存 copula 的样本，相对于通常的随机顺序，较小的主化形状参数向量导致较小的样本最大值和较大的样本最小值。提供了几个数值例子和一个应用来说明理论发现。