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Order preserving measures of information

Published online by Cambridge University Press:  14 July 2016

S. G. S. Shiva ,
N. U. Ahmed  and
N. D. Georganas
N. D. Georganas
Affiliation:
The University of Ottawa
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Abstract

If the information content of a complete finite probability scheme is greater than that of another such scheme in one measure of information, it seems reasonable to expect that this relation remains true in any other valid measure. In this paper Shannon and Rényi measures are discussed, regarding this aspect.

Keywords

INFORMATION MEASURESAXIOMATICSORDER PRESERVINGRÉNYI ENTROPYSHANNON ENTROPYNEW POSTULATE
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 3 , September 1973 , pp. 666 - 670
Copyright
Copyright © Applied Probability Trust 1973 

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Footnotes

Research supported in part by the National Research Council of Canada under Grants A-3371, A-7109 and A-8450. Some of the results of this paper were presented at the 1971 International Conference on Communications, Montreal, under the title “Some results arising from Information Theory”.

References

Aczel, J. (1969) On Different Characterizations of Entropies. Springer Lecture Notes in Math. No. 89.10.1007/BFb0079114Google Scholar
Ash, R. (1965) Information Theory. Interscience Publishers, New York, 5–24.Google Scholar
Campbell, L. L. (1965) A coding theorem and Rényi's entropy. J. of Inform, and Control 8, 423–429.10.1016/S0019-9958(65)90332-3Google Scholar
Kannappan, Pl. (1972) On Shannon's entropy, directed divergence and inaccuracy. Zeit. Wahrscheinlichkeitsth. 22, 95–100.10.1007/BF00532728Google Scholar
Rényi, A. (1961) On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. University of California Press. 1, 547–553.Google Scholar
Shannon, C. E. and Weaver, W. (1949) The Mathematical Theory of Communication. The University of Illinois Press, Urbana. 18–22.Google Scholar