Characterization of exponentiated family of distributions based on recurrence relations for generalized order statistics

Abstract

In this paper, we derive recurrence relations for moment, conditional moment generating functions and product moments of generalized order statistics  based on exponentiated family of distributions. Recurrence relations for moment, conditional moment generating functions and product moments of ordinary order statistics  and ordinary record values  are obtained as special cases. These recurrence relations are also used to characterize this family.