Given a random sample \(X_1, X_2, \ldots , X_n\), the distributions of \(\min \left( X_1, X_2, \ldots , X_n \right)\) and \(\max \left( X_1, X_2, \ldots , X_n \right)\) are of interest in many areas. We derive explicit expressions for moments of \(\min \left( X_1, X_2, \ldots , X_n \right)\) and \(\max \left( X_1, X_2, \ldots , X_n \right)\) for thirty four families of distributions, including the normal and Student’s t distributions. These results can be especially useful when data are scarce. The correctness of the expressions is checked by a simulation study. Applications to two engineering data sets are given.

给定随机样本\（X_1，X_2，\ ldots，X_n \），\（\ min \ left（X_1，X_2，\ ldots，X_n \ right）\）和\（\ max \ left（X_1， X_2，\ ldots，X_n \ right）\）在许多领域都很受关注。我们导出三十分钟\（\ min \ left（X_1，X_2，\ ldots，X_n \ right）\）和\（\ max \ left（X_1，X_2，\ ldots，X_n \ right）\）的显式表达式四个分布族，包括正态分布和学生t分布。当数据稀缺时，这些结果可能特别有用。表达式的正确性通过模拟研究进行检查。给出了对两个工程数据集的应用。