New Characterizations by Properties of Midrange and Related Statistics

New families of distributions are characterized by regressional properties of order statistics. Among equations for regressions based on order statistics X 1:n ,…, X n:n , n = 1, 2,…, we investigate a relation of the form E(λX k:2k+1 + (1 − λ)X k+2:2k+1|X k+1:2k+1 = x) = x, (0 < λ < 1). As a special case, a characterization of Student's t 2 distribution is obtained.