On characterizations based on record values and order statistics

Consider an infinite sequence of independent random variables having common continuous c.d.f. F. For 1 ⩽ i ⩽ n, let X_i:n denote the ith order statistic of the first n random variables, and let {X(n), n ⩾ 1} be the sequence of upper record values. We examine the similarities and differences between the dependence structures of the X_i:n's and the X(n)'s, with an emphasis on the latter. We present an interesting situation involving a characterization of F using the moment sequence of records. We obtain characterizations based on the properties of certain regression functions associated with order statistics, record values, and the original observations. We discuss the resemblance between some known and some new characterizations based on order statistics, record values and those based on the properties of truncated F.