Asymptotic distributions of order statistics and record values arising from the class of beta-generated distributions

In this paper, we show that both the class of beta-generated distributions G_F and its base distribution F belong to the same domain of maximal (or minimal or upper record value or lower record value) attraction. Moreover, it is shown that the weak convergence of any non-extreme order statistic (central or intermediate order statistic), based on a base distribution F, to a non-degenerate limit type implies the weak convergence of G_F to a non-degenerate limit type. The relations between the two limit types are deduced.