Characterization of symmetric distributions based on concomitants of ordered variables from FGM family of bivariate distributions

Abstract

‎Several characterization results of a symmetric distribution based on concomitants of order statistics as well as $k$-records from Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions are established‎. ‎These include characterizations of a symmetric distribution on the basis of equality in distribution‎, ‎moments‎, ‎R\'{e}nyi and Tsallis entropies of concomitants of upper and lower order statistics‎, ‎also in terms of the same properties of concomitants of upper and lower $k$-records‎.