On the limit distribution of lower extreme generalized order statistics

In a wide subclass of generalized order statistics (gOs), which contains most of the known and important models of ordered random variables, weak convergence of lower extremes are developed. A recent result of extreme value theory of m -gOs (as well as the classical extreme value theory of ordinary order statistics) yields three types of limit distributions that are possible in case of linear normalization. In this paper a similar classification of limit distributions holds for extreme gOs, where the parameters gamma (j) ,j = 1, . . . , n, are assumed to be pairwise different. Two illustrative examples are given to demonstrate the practical importance for some of the obtained results.