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The noncentral F-distribution, which yields the power function of tests of linear hypotheses as in the analysis of variance and of covariance, is computed by numerical integration of a contour integral in the complex plane. Determining the percentage points of this distribution is facilitated by approximating the integral by Laplace’s method during the initial stages of a search by the secant method.
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Helstrom et al. (1985) studied this question.
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