© 1966 by Biometrika Trust
Exact distributions of Wilks's likelihood ratio criterion
IBM Scientific Center Cambridge, Massachusetts
The null distributions of Wilks's likelihood ratio criterion
are derived, and it is shown that the density and distribution functions of
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
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.
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