On characterization of distributions through the properties of conditional expectations of order statistics

Abstract

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 X-1:m:n(R), X-2:m:n(R),..., X-m:m:n(R) 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 X-1:m:n(R),..., X-m:m:n(R) can be reduced to the joint distribution of usual order statistics of a sample size m from a continuous random variable.