Title: Results related to exponential entropy

Authors: Sajjad Mazloum Panjehkeh; Gholam Reza Mohtashami Borzadaran; Mohammad Amini

Addresses: Department of Statistics and Ordered and Spatial Data Center of Excellence, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran ' Department of Statistics and Ordered and Spatial Data Center of Excellence, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran ' Department of Statistics and Ordered and Spatial Data Center of Excellence, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract: The Shannon entropy which is widely used in many fields of science, some advantage and disadvantage of it are noticeable. In view of disadvantage formulated, other entropies like exponential entropy. In this paper, we study some characterisation and properties of exponential entropy such as asymptotic equipartition property, chain rule, the subadditivity, invariancy under monotone transformation in parallel to those for the Shannon entropy in continuous and discrete cases. Also, the relationship between exponential entropy with Tsallis entropy and Renyi entropy obtained. Finally, we show that in the image segmentation, algorithms based on exponential entropy has a better performance than the algorithms which are based on the Shannon entropy.

Keywords: chain rule; exponential entropy; information theory; jensen's inequality; Shannon entropy; Tsallis entropy.

DOI: 10.1504/IJICOT.2017.086915

International Journal of Information and Coding Theory, 2017 Vol.4 No.4, pp.258 - 275

Received: 16 Dec 2016
Accepted: 09 Feb 2017
Published online: 02 Oct 2017 *

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