Summary
Some characterization theorems are given for the various generalized measures of information and uncertainty by using two types of functional inequalities. This paper unifies several existing results on the various measures of information and some special cases of interest are mentioned at appropriate places.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aczél, J. andZ. Daróczy: Measures of information and their characterizations, Academic Press, New York, 1972 — In Preparation.
Aczél, J. ansZ. Daróczy: Über verallgemeinerte quasilineare Mittelwerte, die mit Gewichtsfunktionen gebildet sind, Publ. Math., Debrecen,10, 171–190, 1963.
Aczél, J. andJ. Pfanzagl: Remarks on the measurement of subjective probability and information, Metrika,11, 91–105, 1966.
Campbell, L. L.: Equivalence of Gauss' Principle and minimum information estimation of probabilities, Ann. Math. Statist.41, 1011–1015, 1970.
Daróczy, Z.: Generalized information functions, Information and Control,16, 36–51, 1970.
Fischer, P.: On the inequality Σp i f(p i )≧Σp if(qi), Metrika,18/2, p. 199-208.
Hardy, G.H., J.E. Littlewood andG. Pólya: Inequalities, Cambridge University Press, 1934.
Havrda, J. andF. Charvát: Quantification method of classification processes. The concept of structural a-entropy, Kybernetika,3, 30–35, 1967.
Kapur, J.N.: Generalized entropy of order α and type β, Math Seminar, Delhi,4, 78–94, 1967.
Kapur, J.N.: Information of order α and type β, Proc. Indian Acad. Sci. A68, 65–75, 1968.
Kullback, S.: Information theory and statistics, John Wiley and Sons, New York, 1959.
Muszély, Gy.: On continuous solutions of a functional inequality, Unpublished report.
Natanson, I.P.: Theory of functions of a real variable, Vol. I, Frederick Ungar Publishing Co., New York 1964.
Rathie, P.N. andP.L. Kannappan: A directed divergence function of type β, Information and control,20, 38–45, 1972.
Rathie, P.N.: On a generalized entropy and a coding theorem. J. Appl. Prob.,7, 124–133, 1970.
Rathie, P.N.: On generalized measures of inaccuracies, information and errors in information, Statistica,30, 340–349, 1970.
Rényi, A.: On measures of entropy and information, Proc. Fourth Berkeley Symp. Math. Statist. and Prob.,1, 547–561, 1961.
Shannon, C.E.: A mathematical theory of communication, Bell Syst. Techn. J.,27, 378–423 and 623–656, 1948.
Vajda, I.: Axioms of a-entropy of a generalized probability distribution, Kybernetika,4, 105–110, 1968.
Author information
Authors and Affiliations
Additional information
The work of this paper was done while the author was a visiting postdoctoral fellow with the University of Waterloo. This paper was presented at the Meeting on Information Measures held at the University of Waterloo, Waterloo, Ontario, Canada from April 10–14, 1970.
Rights and permissions
About this article
Cite this article
Rathie, P.N. Some characterization theorems for generalized measures of uncertainty and information. Metrika 20, 122–130 (1973). https://doi.org/10.1007/BF01893811
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01893811