RESULTS ON TSALLIS ENTROPY OF ORDER STATISTICS AND RECORD VALUES

Abstract

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

Keywords

• Characterization, Hazard rate function, Muntz-Szasz theorem, Series (parallel) system,Symmetric distributions, Tsallis information

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