MATHEMATICAL ENGINEERING TECHNICAL REPORTS Holonomic Gradient Method for the Distribution Function of the Largest Root of a Wishart Matrix
نویسندگان
چکیده
We apply the holonomic gradient method introduced by Nakayama et al. [19] to the evaluation of the exact distribution function of the largest root of a Wishart matrix, which involves the hypergeometric function 1F1 of a matrix argument. Compared to methods based on infinite series expansion in terms of zonal polynomials, whose convergence is slow, the proposed method is more practical for computing upper tail probabilities. We show that our proposed method works well up to dimension 10.
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