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Entropy 2013, 15(10), 4011-4025; doi:10.3390/e15104011
Article

On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data

1,2
 and 3,4,*
1 Centre for Mathematical Sciences, Arunapuram P.O., Palai, Kerala 686574, India 2 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec H3A2K6, Canada 3 Centre for Mathematical Sciences, Arunapuram P.O., Palai, Kerala 686574, India 4 Office for Outer Space Affairs, United Nations, Vienna International Centre, P.O. Box 500, Vienna A-1400, Austria
* Author to whom correspondence should be addressed.
Received: 4 September 2013 / Accepted: 22 September 2013 / Published: 25 September 2013
(This article belongs to the Special Issue Dynamical Systems)
Download PDF [257 KB, 24 February 2015; original version 24 February 2015]

Abstract

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided.
Keywords: generalized entropy; scalar, vector, and matrix cases; optimization; mathematical and statistical models; pathway model; non-extensive statistical mechanics; solar neutrino data; diffusion entropy analysis; standard deviation analysis generalized entropy; scalar, vector, and matrix cases; optimization; mathematical and statistical models; pathway model; non-extensive statistical mechanics; solar neutrino data; diffusion entropy analysis; standard deviation analysis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Mathai, A.M.; Haubold, H.J. On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data. Entropy 2013, 15, 4011-4025.

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