An alternative notion of entropy called CRE is proposed in [Ra1] Rao et al. (IEEE Trans. Inf. Theory 50, 2004). This preserves many of the properties of Shannon Entropy and possesses mathematical properties, which we hope will be of use in statistical estimates. In this article, we develop some more mathematical properties of CRE, show its relation to the L log L class, and characterize among others the Weibull distribution.
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References
T. M. Cover J. A. Thomas (1991) Elements of Information Theory Wiley New York
H. Federer (1969) Geometric Measure Theory Springer Berlin
Grendar M. Jr., and Grendar M. (2000). What is the Question that MaxEnt answers? Bayesian Inference And Maximum Entropy Methods In Science and Engineering. 20th International Workshop Gif-sur-Yvette, France. Ed. Ali Mohammad-Djafari American Institute of Physics Conference Proceedings 568.
Jumarie G. (1990). Relative Information, Springer.
Kalbfleisch J. D., and Prentice R. L. (1980). The Statistical Analysis of Failure Time Data Wiley Series in Probability.
J. N. Kapur (1989) Maximum Entropy Methods in Science and Engineering Wiley New York
M. A. Krasnoselskli Ya.B. Rutickii (1961) Convex Functions and Orlicz Spaces Noordhoff Leiden
R. O’Neil (1966) ArticleTitleLes fonctiones conjugues et les integrales fractionnaires de la classe Llog+, L C.R. Acad.Sci.Paris 263 463–466
Rao M., Chen Y., Vemuri B., and Fei W. (2004). Cumulative residual entropy : a new measure of information. IEEE Trans.Inf.Theory 50.
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Tech.J. 27, 379–423, 623–656.
E. M. Stein (1969) ArticleTitleNote on the Class L log L Studia Math. 32 305–310
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Rao, M. More on a New Concept of Entropy and Information. J Theor Probab 18, 967–981 (2005). https://doi.org/10.1007/s10959-005-7541-3
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DOI: https://doi.org/10.1007/s10959-005-7541-3