Distributions of Lawley-Hotelling's T₀² and Related Statistics: A Review

SYNOPTIC ABSTRACT

In this review article on the distributions of Lawley–Hotelling's T₀² and related statistics, the following topics are reviewed and discussed: (1) exact distributions, (2) system of partial differential equations related to T₀², (3) asymptotic expansions for the distribution of T₀² by several methods, (4) percentage points and tables, and (5) miscellanea (including the distributions of two T₀² statistics and their ratio and the maximum of ordinary T²'s). T₀² in this paper is the test statistic for noncentrality due to population mean vectors, i.e. the MANOVA test statistic. However the discussion for the central case is valid for the null cases of equality of two population covariance matrices and the independence of two sets of variates.

Key Words and Phrases:

• asymptotic expansions
• exact distributions
• generalized hypergeometric function
• generalized Laguerre polynomials
• Lawley–Hotelling's T₀²
• percentage points
• Pillai's trace
• system of partial differential equations
• zonal polynomials