COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 723R

"An Everywhere Convergent Series Representative
of the Distribution of Hotelling's Generalized T₀²"

Peter C.B. Phillips

September 1984
Revised March 1986

A new series representation of the exact distribution of Hotelling's generalized T₀² statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the noncentral distributions. Earlier results by Constantine [1], which are convergent on the interval [0,1), are also derived quite simply from our formulae.

JEL Classification: 62H10, 62E15

Keywords: Hotelling's T₀², exact distribution, invariant polynomials, everywhere convergent series

See CFP 675