Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy–Widom distribution

Marco Chiani

Journal of Multivariate Analysis, 2014, vol. 129, issue C, 69-81

Abstract: We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy–Widom law can be approximated by a properly scaled and shifted gamma distribution, with great accuracy for the values of common interest in statistical applications.

Keywords: Random matrix theory; Characteristic roots; Largest eigenvalue; Tracy–Widom distribution; Wishart matrices; Gaussian Orthogonal Ensemble (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2014.04.002

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