On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains
This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the <i>y&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/11/1534 |
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| author | Princy Thankamani Nicy Sebastian Hans J. Haubold |
| author_facet | Princy Thankamani Nicy Sebastian Hans J. Haubold |
| author_sort | Princy Thankamani |
| collection | DOAJ |
| description | This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the <i>y</i>-mean by de Finetti and hypergeometric mean by Carlson; see the references herein. Carlson’s hypergeometric mean averages a scalar function over a real scalar variable type-1 Dirichlet measure, which is known in the current literature as the Dirichlet average of that function. The idea is examined when there is a type-1 or type-2 Dirichlet density in the complex domain. Averages of several functions are computed in such Dirichlet densities in the complex domain. Dirichlet measures are defined when the matrices are Hermitian positive definite. Some applications are also discussed. |
| first_indexed | 2024-03-09T16:50:38Z |
| format | Article |
| id | doaj.art-2fef2c7435bf43098ce4832159583148 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T16:50:38Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-2fef2c7435bf43098ce48321595831482023-11-24T14:41:03ZengMDPI AGEntropy1099-43002023-11-012511153410.3390/e25111534On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-DomainsPrincy Thankamani0Nicy Sebastian1Hans J. Haubold2Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, IndiaDepartment of Statistics, St. Thomas College Thrissur, Calicut University, Thenhipalam 680 001, IndiaOffice for Outer Space Affairs, United Nations, Vienna International Center, A-1400 Vienna, AustriaThis paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the <i>y</i>-mean by de Finetti and hypergeometric mean by Carlson; see the references herein. Carlson’s hypergeometric mean averages a scalar function over a real scalar variable type-1 Dirichlet measure, which is known in the current literature as the Dirichlet average of that function. The idea is examined when there is a type-1 or type-2 Dirichlet density in the complex domain. Averages of several functions are computed in such Dirichlet densities in the complex domain. Dirichlet measures are defined when the matrices are Hermitian positive definite. Some applications are also discussed.https://www.mdpi.com/1099-4300/25/11/1534Dirichlet averagegeneralized type-1type-2 Dirichlet measuresfunctions of matrix argumentDirichlet measures in the complex domain |
| spellingShingle | Princy Thankamani Nicy Sebastian Hans J. Haubold On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains Entropy Dirichlet average generalized type-1 type-2 Dirichlet measures functions of matrix argument Dirichlet measures in the complex domain |
| title | On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains |
| title_full | On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains |
| title_fullStr | On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains |
| title_full_unstemmed | On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains |
| title_short | On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains |
| title_sort | on complex matrix variate dirichlet averages and its applications in various sub domains |
| topic | Dirichlet average generalized type-1 type-2 Dirichlet measures functions of matrix argument Dirichlet measures in the complex domain |
| url | https://www.mdpi.com/1099-4300/25/11/1534 |
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