Distribution of Wilks' likelihood-ratio criterion in the complex case

Summary The null distribution of Wilks' likelihood ratio criterian, Λ, in the complex case, is obtained, and explicit expressions for the same are given forp=2 and 3, wherep is the number of variables. It is shown that unlike the real case the distributions derived have closed form representation for allp and for allf ₂, the hypothesis degree of freedom. Tables of correction factors for converting chi-square percentiles to exact percentiles of a logarithmic function of Λ are provided for fourteen (p, f ₂) pairs. Tables for an additional thirteen pairs can be obtained from those tabulated by interchangingp andf ₂. This research was supported (in part) by the National Science Foundation under Grant Number GU-15-34. Reproduction in whole or in part is permitted for any purpose of the United States Government.