In this paper the exact distribution of Wilks' likelihood ratio criterion for testing linear hypothesis about regression coefficients is discussed. The exact distribution, in the most general case, is given in simple algebraic functions which can be computed without much difficulty. Explicit expressions for the density function as well as for the cumulative distribution function are given under the null hypothesis.
A. M. Mathai. P. N. Rathie. "The Exact Distribution of Wilks' Criterion." Ann. Math. Statist. 42 (3) 1010 - 1019, June, 1971. https://doi.org/10.1214/aoms/1177693329