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EnglishWe 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.
| Titolo: | Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy–Widom distribution |
| Autore/i: | CHIANI, MARCO |
| Autore/i Unibo: | |
| Anno: | 2014 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmva.2014.04.002 |
| 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. |
| Data prodotto definitivo in UGOV: | 2014-10-27 15:04:26 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11585/280113
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