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On characterization of a generalized inaccuracy measure in information theory

Published online by Cambridge University Press:  14 July 2016

Bhu Dev Sharma  and
Ram Autar
Bhu Dev Sharma
Affiliation:
University of Delhi
Ram Autar*
Affiliation:
University of Delhi
*
* This author is grateful to C.S.I.R. (India) for financial assistance.
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Abstract

Sharma and Autar [6] have formed a functional equation in two variables containing two parameters which, as a particular case, includes Daróczy's [1] generalized functional equation used in information theory. The solutions of our functional equation, under suitable boundary conditions, lead to an inaccuracy function of a new type. A characterization of this inaccuracy function and the convexity of Daróczy's entropy of type-ß have been given in this paper.

Keywords

INFORMATION THEORYFUNCTIONAL EQUATIONENTROPY FUNCTIONINACCURACY FUNCTIONGENERALIZED INACCURACY FUNCTIONCONVEXITY OF GENERALIZED ENTROPY

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 464 - 468
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Daróczy, Z. (1970) Generalized information functions. Information and Control 16, 36–51.CrossRefGoogle Scholar
[2] Kendall, D. G. (1964) Functional equations in information theory. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, 225–229.Google Scholar
[3] Kerridge, D. F. (1961) Inaccuracy and inference. J. R. Statist. Soc. B 23, 184–194.Google Scholar
[4] Shannon, C. E. (1948) A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423. Reprinted in Shannon, C. E. and Weaver, W. (1964) The Mathematical Theory of Communication. Univ. of Illinois Press, Urbana, Ill Google Scholar
[5] Sharma, B. D. and Autar, R. (1972) Functional equation of two variables in information theory. Submitted.Google Scholar
[6] Sharma, B. D. and Autar, R. (1973) Generalized functional equation of two variables in information theory. Rev. Française d'lnformatique et de Rech. Operationnelle (Paris) R 3.Google Scholar