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We study the distribution of the ratio of two central Wishart matrices withdifferent covariance matrices. We first derive the density function of aparticular matrix form of the ratio and show that its cumulative distributionfunction can be expressed in terms of the hypergeometric function 2F1 of amatrix argument. Then we apply the holonomic gradient method for numericalevaluation of the hypergeometric function. This approach enables us to computethe power function of Roy's maximum root test for testing the equality of twocovariance matrices.

Distribution of ratio of two Wishart matrices and evaluation of cumulative probability by holonomic gradient method