Nonnull distribution of Wilks' statistic for Manova in the complex case

In this paper, the exact distribution of Wilks' likelihood ratio criterion, A, for MANOVA, in the complex case when the alternate hypothesis is of unit rank (i.e. the linear case) has been derived and the explicit expressions for the same for p = 2 and 3 (where p is the number of variates) and general f₁ (the error degrees of freedom) and f₂ (the hypothesis degrees of freedom), are given. For an unrestricted number of variables, a general form of the density and the distribution of A in this case, is also given. It has been shown that the total integral of the series obtained by taking a few terms only, rapidly approaches the theoretical value one as more terms are taken into account, and some percentage points have also been computed.