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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