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Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix


Vlok, JD and Olivier, JC, Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix, Institution of Engineering and Technology Communications, 6, (12) pp. 1804-1811. ISSN 1751-8628 (2012) [Refereed Article]

Copyright Statement

Copryright 2012 The Institution of Engineering and Technology

DOI: doi:10.1049/iet-com.2011.0843


Eigenvalue distributions of Wishart matrices are given in the literature as functions or distributions defined in terms of matrix arguments requiring numerical evaluation. As a result the relationship between parameter values and statistics is not available analytically and the complexity of the numerical evaluation involved may limit the implementation, evaluation and use of eigenvalue techniques using Wishart matrices. This study presents analytic expressions that approximate the distribution of the largest eigenvalue of white Wishart matrices and the corresponding sample covariance matrices. It is shown that the desired expression follows from an approximation to the Tracy-Widom distribution in terms of the Gamma distribution. The approximation offers largely simplified computation and provides statistics such as the mean value and region of support of the largest eigenvalue distribution. Numeric results from the literature are compared with the approximation and Monte Carlo simulation results are presented to illustrate the accuracy of the proposed analytic approximation. © 2012 The Institution of Engineering and Technology.

Item Details

Item Type:Refereed Article
Research Division:Engineering
Research Group:Communications engineering
Research Field:Signal processing
Objective Division:Information and Communication Services
Objective Group:Communication technologies, systems and services
Objective Field:Mobile technologies and communications
UTAS Author:Olivier, JC (Professor JC Olivier)
ID Code:82335
Year Published:2012
Web of Science® Times Cited:6
Deposited By:Engineering
Deposited On:2013-01-25
Last Modified:2017-11-06
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