On 'Useful' Relative Information Measures of Order α and Type β

10.6186/IJIMS.2013.24.2.1

Satish Kumar；Arun Choudhary；Gurdas Ram；Vishal Gupta

Relative information measure ； 'Useful' information measure ； Havrda-Charvat entropy ； Renyi's entropy

International Journal of Information and Management Sciences

24:2（2013 / 06 / 01）

95 - 106

英文

In this paper some new generalized measures of 'useful' relative information have been defined and their particular cases have been studied. From these measures new 'useful' information measures have also been derived and their relations with different measures of entropy have been obtained.

1. Aczel, J.,Daroczy, Z.(1963).Uber Verallgemeinerte quasilineare mittelwerte, die mit Gewichtsfunktionen gebildet sind.Publicationes Mathematicae Debrecen,10,171-190.
2. Behra, M.,Chawla, J. S.(1974).Generalized gamma entropy.Selecta Statistica Canadiana,2,205-215.
3. Belis, M.,Guiasu, S.(1968).A quantitative-qualitative measure of information in cybernetic systems.IEEE Transactions on Information Theory,14,593-594.
4. Bhaker, U. S.,Hooda, D. S.(1993).Mean value characterization of ‘useful’ information measures.Tamkang Journal of Mathematics,24,383-394.
5. Havrda, J. F.,Charvat, F.(1967).Qualification Method of Classification Process, the concept of structural α-entropy.Kybernetika,3,30-35.
6. Hooda, D. S.(1986).On generalized measure of relative ‘useful’ information.Soochow Journal of Mathematics,12,23-32.
7. Hooda, D. S.,Ram, A.(2002).On ‘useful’ relative information and J-divergence measures.Tamkang Journal of Mathematics,33,149-160.
8. Hooda, D. S.,Sharma, D. K.(2009).Generalized useful’ information generating functions.Journal of Applied Mathematics & Informatics,27,591-601.
9. Kapur, J. N.(1985).Maximum Entropy Models in Science and Engineering.New Delhi:Wiley Eastern.
10. Kapur, J. N.(1967).Generalized entropy of order α and type β.Math Seminar,4,78-94.
11. Kerridge, D. F.(1961).Inaccuracy and inference.Journal of the Royal Statistical Society. Series B (Methodological),23,184-194.
12. Kullback, S.(1959).Information Theory and Statistics.New York:Wiley.
13. Kullback, S.,Leibler, R. A.(1951).On information and sufficiency.The Annals of Mathematical Statistics,22,79-86.
14. Longo, G.(1976).A noiseless coding theorem for source having utilities.SIAM Journal on Applied Mathematics,30,739-748.
15. Nath, P.,Mittal, D. P.(1973).A generalization of Shannon’s inequality and its application in coding theory.Information and Control,23,439-445.
16. Rathie, P. N.(1971).Generalization of the Non-additive measures of uncertainty and information and their Axiomatic characterization.Kybernetika,7,125-132.
17. Rathie, P. N.,Kannappan, P. I.(1972).A Directed-Divergence function of type β.Information and Control,20,38-45.
18. Renyi, A.(1966).On measures of entropy and information.Proc. 4th Barkley Symp. on Mathematical Statistics and Probability
19. Shannon, C. E. (1948). A Mathematical Theory of Communication, Bell System Technical Journal, Vol.27, 379-423, 623-656.
20. Sharma, B. D.(1975).On account of type β and other measure.Metrika,19,1-10.
21. Tsallis, C.(1988).Possible Generalization of Boltzmann Gibbs Statistics.Journal of Statistical Physics,52,479-487.

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