Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions
In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second au...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/23/6/754 |
| _version_ | 1797530047984173056 |
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| author | Nicy Sebastian Arak M. Mathai Hans J. Haubold |
| author_facet | Nicy Sebastian Arak M. Mathai Hans J. Haubold |
| author_sort | Nicy Sebastian |
| collection | DOAJ |
| description | In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations. |
| first_indexed | 2024-03-10T10:23:23Z |
| format | Article |
| id | doaj.art-4f0be6510d5f486994f18adfd801da0a |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T10:23:23Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-4f0be6510d5f486994f18adfd801da0a2023-11-22T00:13:50ZengMDPI AGEntropy1099-43002021-06-0123675410.3390/e23060754Entropy Optimization, Maxwell–Boltzmann, and Rayleigh DistributionsNicy Sebastian0Arak M. Mathai1Hans J. Haubold2Department of Statistics, St. Thomas College, Thrissur, Kerala 680001, IndiaDepartment of Mathematics and Statistics, McGill University, Montreal, QC H0H H9X, CanadaOffice for Outer Space Affairs, United Nations, Vienna International Center, A-1400 Vienna, AustriaIn physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.https://www.mdpi.com/1099-4300/23/6/754complex Maxwell–Boltzmann and Rayleigh densitiesmultivariate and matrix-variate densitiesmatrix-variate pathway modelstype-1, type-2 beta densitiesgeneralized gammageneralized entropy |
| spellingShingle | Nicy Sebastian Arak M. Mathai Hans J. Haubold Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions Entropy complex Maxwell–Boltzmann and Rayleigh densities multivariate and matrix-variate densities matrix-variate pathway models type-1, type-2 beta densities generalized gamma generalized entropy |
| title | Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions |
| title_full | Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions |
| title_fullStr | Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions |
| title_full_unstemmed | Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions |
| title_short | Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions |
| title_sort | entropy optimization maxwell boltzmann and rayleigh distributions |
| topic | complex Maxwell–Boltzmann and Rayleigh densities multivariate and matrix-variate densities matrix-variate pathway models type-1, type-2 beta densities generalized gamma generalized entropy |
| url | https://www.mdpi.com/1099-4300/23/6/754 |
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