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Entropy of type \((\alpha,\beta)\) and other generalized measures in information theory. (English) Zbl 0328.94012


MSC:

94A15 Information theory (general)

References:

[1] Aczel, J.: Lectures on Functional Equations and their Applications. New York 1966.
[2] Chaundy, T.W., andJ.B. McLeod: On a Functional Equation. Proc. Edin. Math. Soc. Edin. Math. Notes No.43, pp. 7–8, 1960. · Zbl 0100.32703
[3] Daroczy, Z.: Generalized information functions. Information and Control,16, 35–51, 1970. · Zbl 0205.46901 · doi:10.1016/S0019-9958(70)80040-7
[4] Havrda, J., andF. Charvat: Quantification method of classification processes. The concept of Structural a-entropy. Kybernetika,3, 30–35, 1967. · Zbl 0178.22401
[5] Kannappan, Pl.: On Shannon’s entropy, Directed-Divergence and Inaccuracy, Z. Wahrs. Verw. Geb.22, 95–100, 1972. · Zbl 0241.94020 · doi:10.1007/BF00532728
[6] Kerridge, D.F.: Inaccuracy and inference, J. Royal Statist. Soc. Ser. B23, 184–194, 1961. · Zbl 0112.10302
[7] Kullback, S.: Information Theory and Statistics. New York 1959. · Zbl 0088.10406
[8] Rathie, P.N., andPl. Kannappan: A Cirected-Divergence Function of Type {\(\beta\)}. Information and Control,20, 38–45, 1972. · Zbl 0231.94015 · doi:10.1016/S0019-9958(72)90260-4
[9] Shannon, C.E.: A mathematical theory of communication. Bell System Tech. J.27, 379–656, 1948. · Zbl 1154.94303
[10] Sharma, B.D., andRam Autar: On Characterization of a Generalized Inaccuracy Measures in Information Theory. J. of Applied Prob. Vol.10, 464–468, 1973. · Zbl 0261.94024 · doi:10.2307/3212366
[11] –: Relative Information Functions and their Type ({\(\alpha\)}, {\(\beta\)}) Generalizations. Metrika21, (1), 41–50, 1974. · Zbl 0277.94012 · doi:10.1007/BF01893891
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