Characterizations of Student's t-distribution via regressions of order statistics

摘要

Utilizing regression properties of order statistics, we characterize a family of distributions introduced by Akhundov et al. [New characterizations by properties of midrange and related statistics, Commun. Stat. Theory Methods 33(12) (2004), pp. 3133-3143], which includes the t-distribution with two degrees of freedom as one of its members. Then we extend this characterization result to t-distribution with more than two degrees of freedom.