On Characterization of Distributions Through the Properties of Conditional Expectations of Order Statistics

For a general class of distributions some characterizations through the properties of conditional expectations of order statistics and progressively Type-II censored order statistics are given. Let X 1:n , X 2:n ,…, X n:n be the order statistics of the sample X 1, X 2,…, X n from a continuous distribution and be the progressively Type-II censored order statistics with the progressively Type-II censoring scheme R = (R, R,…, R). We show that in this case, the joint distribution of can be reduced to the joint distribution of usual order statistics of a sample size m from a continuous random variable.