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This paper discusses the computation of exact powers for Roy's test inmultivariate analysis of variance~(MANOVA). We derive an exact expression forthe largest eigenvalue of a singular noncentral Beta matrix in terms of theproduct of zonal polynomials. The numerical computation for that distributionis conducted by an algorithm that expands the product of zonal polynomials as alinear combination of zonal polynomials. Furthermore, we provide an exactdistribution of the largest eigenvalue in a form that is convenient fornumerical calculations under the linear alternative.

Numerical computation for the exact distribution of Roy's largest root statistic under linear alternative