Characterization of symmetric distributions based on concomitants of ordered variables from FGMs 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, Rényi 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.

Some characterizations of continuous symmetric distributions based on extropy of record values

“…Hence, a goodness-of-fit test for symmetry can be constructed using characterization results, see, for example, Dai et al (2018) and Bozin et al (2020) and references therein. Characterizations of symmetric distribution are given by many researchers, see Ahmadi and Fashandi (2019), Ahmadi(2019Ahmadi( , 2020, Ushakov (2011), andAhmadi et al (2020). One of the possible applications of the characterization could be testing for symmetry.…”