On the differential equation for Meijer's function, and further tables of Wilks's likelihood ratio criterion

Abstract

The null distributions of a number of likelihood ratio criteria are well known to be expressible in terms of Meijer's function. It is shown that such distributions correspond to a single fundamental solution of the differential equation for this function at the regular singularity one. Computation of percentage points of Wilks's likelihood ratio criterion by analytic continuation of this solution fills some gaps in the previously published tables.