The Tsallis entropy is a generalization of type α of the Shannon entropy (Tsallis, 1988) that is a non-additive entropy unlike the Shannon entropy and some of other generalized entropy, such as Renyi entropy that introduced by Renyi (1961). In this paper, we study the Tsallis entropy based on order statistics and record values.We show that the parent distributions can be determined uniquely by the equality of Tsallis entropy of order statistics or record values. Also, we characterize symmetric distributions based on Tsallis entropy of order statistics and record values. Finally, we prove that the Tsallis information between order statistics and parent random variable, and Tsallis information between record values and parent random variable are distribution free. The results are useful in modeling problems and testing statistical hypotheses.

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