On the Exact Distribution of Pillai's V^(s) Criterion

Abstract

The mgf of Pillai's V ^(s) criterion in the central case has been obtained as a weighted sum of determinants whose elements are incomplete gamma functions. A method is given to reduce the determinants in terms of single integrals or their products. Exact upper 5 and 1 percent points are given for V^{( 3)} and V ⁽⁴⁾ (for selected values of an argument n) using the expressions of the cdf obtained by inversion from the mgf for values of another argument m = 1, 2, 3 for s =3, and m = 0, 1 for s = 4.