Exact distributions of Wilks's likelihood ratio criterion

The null distributions of Wilks's likelihood ratio criterion Λ are derived, and it is shown that the density and distribution functions of Λ have exact closed form representations when p, the number of variates, or q, the hypothesis degrees of freedom. are even. Tables of correction factors for converting chi-square percentiles to exact percentiles of a logarithmic function of Λ are provided in the appendix for twenty-two (p, q) paris. Tables for an additional nineteen pairs can be obtained from those tabulated by interchanging p and q. Finally, it si shown that reasonably accurate approximations can be obtained by linear interpolation fork intermediate cases where p and q are both odd.