‎We introduce here a new and general class of symmetric models‎, ‎referred to as the q-symmetric family of distributions‎. ‎The proposed framework includes several well-known symmetry structures‎, ‎such as the classical location-symmetric‎, ‎log-symmetric‎, ‎and Mobius-symmetric families‎, ‎as special cases‎. ‎We then discuss the theoretical characterization of $q$-symmetric distributions and their relationships to existing symmetry concepts‎. ‎Next‎, ‎using some properties of order statistics‎, ‎we characterize these distributions based on a range of information-theoretic measures associated with the probability density function‎. ‎In particular‎, ‎they include Shannon‎, ‎Renyi‎, ‎and Tsallis entropies as well as their information generating functions‎, ‎extropy and weighted extropy‎, ‎to enunciate some links between symmetry‎, ‎information measures‎, ‎and properties of order statistics‎.

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