Some New Tables of the Largest Root of a Matrix in Multivariate Analysis: a Computer Approach from 2 to 6

The distribution of the non-null characteristic roots of a matrix derived from sample observations taken from multivariate normal populations is of fundamental of importance in multivariate analysis. The Fisher-Girshick-Shu-Roy distribution (1939), which has interested statisticians for more than 6 decades, is revisited. Instead of using K.C.S. Pillai’s method by neglecting higher order terms of the cumulative distribution function (CDF) of the largest root to approximate the percentage points, we simply keep the whole CDF and apply its natural nondecreasing property to calculate the exact probabilities. At the duplicated percentage points, we found our computed percentage points consistent with the existing tables. However, our tabulations have greatly extended the existing tables.