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On functional equations and measures of information. II

Published online by Cambridge University Press:  14 July 2016

PL. Kannappan  and
C. T. Ng
PL. Kannappan*
Affiliation:
University of Waterloo
C. T. Ng*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada.
∗Postal address: Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ont. N2L 3G1, Canada.
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Abstract

We derive the representation of additive measures of information with the sum property under a regular generating function. This family of measures includes the Shanon entropy, directed/symmetric divergence and inaccuracy.

Keywords

ENTROPYMEASURES OF INFORMATIONPROBABILITY DISTRIBUTIONSREPRESENTATION THEOREMADDITIVITYSUM PROPERTY
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 271 - 277
Copyright
Copyright © Applied Probability Trust 1980 

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References

Aczél, J. and Daróczy, Z. (1975) On Measures of Informations and Their Characterizations. Academic Press, New York.Google Scholar
Daróczy, Z. and Jarai, A. (1977) On the measurable solutions of a functional equation of the information theory.Google Scholar
Kannappan, Pl. and Ng, C. T. (1977) On functional equations and measures of information I. Publ. Math. Debrecen. To appear.Google Scholar