Abstract
In this paper, we obtain recurrence relations for moment and conditional moment generating functions of generalized order statistics (gos) based on random samples drawn from a population whose distribution is a member of a doubly truncated class of distributions denoted by F[subscript d]. Members of the class F[subscript d] are characterized in Section (2) based on recurrence relations for moment generating functions (moments) of gos. In Section (3), we shall characterize members of the class F[subscript d] based on recurrence relations for conditional moment generating functions (conditional moments) of gos. These results are specialized to the left, right and non-truncated cases. Ordinary order statistics and ordinary record values are also obtained as special cases of the gos. Characterizations of some members of class F[subscript d] such as the Weibull, compound Weibull, Pareto, power function (beta is a special case), Gompertz and compound Gompertz distributions are given as illustrative examples.