On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/10/4011 |
| _version_ | 1798000021997617152 |
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| author | Hans J. Haubold Arak M. Mathai |
| author_facet | Hans J. Haubold Arak M. Mathai |
| author_sort | Hans J. Haubold |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T11:13:38Z |
| format | Article |
| id | doaj.art-0991de6fd1b24c6581fe8a87aa6a33e7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T11:13:38Z |
| publishDate | 2013-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0991de6fd1b24c6581fe8a87aa6a33e72022-12-22T04:27:19ZengMDPI AGEntropy1099-43002013-09-0115104011402510.3390/e15104011On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino DataHans J. HauboldArak M. MathaiAn 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.http://www.mdpi.com/1099-4300/15/10/4011generalized entropyscalar, vector, and matrix casesoptimizationmathematical and statistical modelspathway modelnon-extensive statistical mechanicssolar neutrino datadiffusion entropy analysisstandard deviation analysis |
| spellingShingle | Hans J. Haubold Arak M. Mathai On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data Entropy 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 |
| title | On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data |
| title_full | On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data |
| title_fullStr | On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data |
| title_full_unstemmed | On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data |
| title_short | On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data |
| title_sort | on a generalized entropy measure leading to the pathway model with a preliminary application to solar neutrino data |
| topic | 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 |
| url | http://www.mdpi.com/1099-4300/15/10/4011 |
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