Computation of the null distribution of the largest or smallest latent roots of a beta matrix

An algorithm is presented for the numerical evaluation of the null distribution of the largest latent root of a beta matrix, based on a finite series recently given by Khatri [6]. The same method can also be used for the distribution of the smallest latent root, and it can be easily adapted to find percentage points. The method is only useful if the size of the matrix and the size of the denominator sample are small, and in this sense it complements some of the large sample approximations. Although the calculation may be fairly lengthy, the algorithm itself is quite short, and a Fortran coding of it will be submitted to the Journal of the Royal Statistical Society, Series C (Applied Statistics) for publication.