A generating function and finite Fourier series turn the Pfaffian structure of GOE and LOE into a practical algorithm for all marginal eigenvalue distributions, tested up to N=100.
Chiani, Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution, J
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Computing marginal eigenvalue distributions for the Gaussian and Laguerre orthogonal ensembles
A generating function and finite Fourier series turn the Pfaffian structure of GOE and LOE into a practical algorithm for all marginal eigenvalue distributions, tested up to N=100.