On the maximum and minimum for classes of univariate distributions

Given a random sample $$X_1, X_2, \ldots , X_n$$ X 1 , X 2 , … , X n , the distributions of $$\min \left( X_1, X_2, \ldots , X_n \right)$$ min X 1 , X 2 , … , X n and $$\max \left( X_1, X_2, \ldots , X_n \right)$$ max X 1 , X 2 , … , X n are of interest in many areas. We derive explicit expressions for moments of $$\min \left( X_1, X_2, \ldots , X_n \right)$$ min X 1 , X 2 , … , X n and $$\max \left( X_1, X_2, \ldots , X_n \right)$$ max X 1 , X 2 , … , X n 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.