TABLE FOR UPPER PERCENTAGE POINTS OF THE LARGEST ROOT OF A DETERMINANTAL EQUATION WITH FIVE ROOTS

By William W. Chen.

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

Key Words: Characteristic roots, extended tables, Fisher-Girshick-Hsu-Roy Distribution, Percentage points

Author:
William W. Chen, william.w.chen@irs.gov

Editor: Ahmed S. Ejaz,Ahmed@math.uregina.ca

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