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 y-mean by de...

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Veröffentlicht in:Entropy (Basel, Switzerland) Jg. 25; H. 11; S. 1534
Hauptverfasser: Thankamani, Princy, Sebastian, Nicy, Haubold, Hans J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.11.2023
Schlagworte:
Computational linguistics
Dirichlet average
Dirichlet measures in the complex domain
Dirichlet problem
Domains
functions of matrix argument
generalized type-1
Language processing
Mathematical analysis
Mathematical functions
Matrices (mathematics)
Natural language interfaces
Prime numbers
Probability distribution
type-2 Dirichlet measures
Variables
ISSN:1099-4300, 1099-4300
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Zusammenfassung: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 y-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.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e25111534