Relative information functions and their type (α, β) generalizations
- 23 Downloads
The concept of relative information functions by means of a functional equation under suitable boundary conditions is introduced and discussed. Further the relative information is defined in terms of these functions and this idea is extended to the new concept of relative information functions of type (α, β) (α, β>0, α≠β) and relative information of type (α,β) which are the generalizations of the earlier ones. Finally the different types of relative informations of type (α, β) are defined for bivariate distributions and the relations between them are established.
KeywordsBoundary Condition Stochastic Process Probability Theory Functional Equation Economic Theory
Unable to display preview. Download preview PDF.
- Daróczy, Z.: Generalized Information functions. Information and Control16, 36–51, 1970.Google Scholar
- Gallager, R. G.: Information Theory and reliable communication. John Wiley and Sons, Inc. N. Y. 523–524, 1968.Google Scholar
- Kendall, D. G.: Functional Equations in Information Theory. Z. Wahrscheinlichkeitstheorie verw. Geb.2, 225–229, 1963.Google Scholar
- Kullback, S.: Information Theory and Statistics. John Wiley and Sons, Inc. N. Y. 1959.Google Scholar
- Rathie, P. N., andP. L. Kannappan: A directed divergence function of type-β. Information and Control20, 38–45, 1972.Google Scholar
- Rényi, A.: On measures of entropy and information. Proc. 4th Berkeley Sympos. Math. Staat. and Prob.1, 547–561, 1960.Google Scholar
- Shannon, C. E.: A mathematical theory of communication. Bell system Tech. J.27, 379–423, 1948.Google Scholar
- Sharma, B. D., andR. Autar: On characterization of a generalized inaccuracy measure in Information Theory Jour. of Applied Prob.10, 464–468, 1973.Google Scholar
- Sharma, B. D., andR. Autar: A functional equation of two variables in Information Theory. Unpublished, 1972.Google Scholar
- Tverberg, H.: A new derivation of the Information function. Math. Scand.6, 297–298, 1958.Google Scholar