F approximations to the distribution of Hotelling's T²₀

Abstract

Two F approximations are proposed for the distribution of Hotelling's T²₀. The first approximation fits the first three moments, the second specifies the value of the numerator degrees of freedom and fits the first two moments. The second approximation is slightly better than the first, and improves on F approximations proposed by Pillai & Sampson (1959) and Hughes & Saw (1972).