On distributions of generalized order statistics

In a wide subclass of generalized order statistics, representations of marg inal density and distribution functions are developed. The results are appl ied to obtain several relations, such as recurrence relations, and explicit expressions for the moments of generalized order statistics from Pareto, p ower function and Weibull distributions. Moreover, characterizations of exp onential distributions are shown by means of a distributional identity as w ell as by an identity of expectations involving a subrange and a correspond ing generalized order statistic.