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Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method. (English) Zbl 1397.62188
Summary: We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can be expressed in terms of the hypergeometric function \({}_2 F_1\) of a matrix argument. Then we apply the holonomic gradient method for numerical evaluation of the hypergeometric function. This approach enables us to compute the power function of Roy’s maximum root test for testing the equality of two covariance matrices.

MSC:
62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
62H15 Hypothesis testing in multivariate analysis
Software:
hgm R; Risa/Asir
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