Let Λ=|Se|/|Se+Sh|, where Sh and Se are independently distributed as Wishart distributions Wp(q,Σ) and Wp(n,Σ), respectively. Then Λ has Wilksx2019; lambda distribution Λp,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T