Some characterizations by conditional events of generalized order statistics

Characterizations of distributions based on conditional probability and linear regression have been investigated quite extensively in the literature involving ordered random variables. As generalized order statistics (GOS) provide a unifying approach to models of ordered random variables, we establish here some characterizations on absolutely continuous distributions based on GOS which contain and strengthen several known results in this regard. Because we do not impose restrictions on the model parameters (as done in the most of previous studies), our findings yield new results for various useful models of ordered random variables including k-record values, sequential order statistics, and progressively Type-II censored order statistics with an arbitrary censoring plan.