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unified $(r,s)$-entropy measure; order statistics; Shannon entropy; logistic distribution.

References:

[1] S. Arimoto: **Information-theoric consideration on estimation problems**. Information and Control 19 (1971), 181–194. MR 0309224

[2] N. Balakrishnan and A. C. Cohen: **Order statistics and inference, Estimation methods**. Academic Press, 1991. MR 1084812

[3] I. S. Gradshteyn and I. M. Ryzhik: **Table of integrals, series and products**. Academic Press, 1980. MR 1398882

[4] I. Havrda and F. Charvat: **Quantification method of classification processes: concept of structural $\alpha $-entropy**. Kybernetika 3 (1967), 30–35. MR 0209067

[5] A. Renyi: **On measures of entropy and information**. Proc. 4th Berkeley Symp. Math. Statist. and Prob. 1 (1961), 547–561. MR 0132570 | Zbl 0106.33001

[6] C. E. Shannon: **A mathematical theory of communications**. Bell. Syst. Tech. J. 27 (1948), 379–423. MR 0026286

[7] B. D. Sharma and D. P. Mittal: **New nonadditive measures of entropy for discrete probability distribution**. J. Math. Sci. 10 (1975), 28–40. MR 0539493

[8] I. J. Taneja: **On generalized information measures and their applications**. Adv. Elect. and Elect. Phis. 76 (1989), 327–413.

[9] K. M. Wong and S. Chen: **The entropy of ordered sequences and order statistics**. IEEE Transactions on Information Theory 36(2) (1990), 276–284. MR 1052779