## The Annals of Mathematical Statistics

### Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II

Koichi Ito

#### Abstract

In this paper an asymptotic formula for the cumulative distribution function (c.d.f.) of Hotelling's generalized $T_0^2$ statistic is derived for general values of the number of dimensions in the non-null case. This result includes as a special case the previous result of the author for the null distribution of $T_0^2$ [5], and shows certain properties of $T_0^2$ which help determine the power of the test based on the statistic for moderately large samples. Both of the author's results provide an approximate complete analysis of the $T_0^2$ test, although the exact null and non-null distributions of $T_0^2$ are not available at present.

#### Article information

Source
Ann. Math. Statist., Volume 31, Number 4 (1960), 1148-1153.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177705685

Digital Object Identifier
doi:10.1214/aoms/1177705685

Mathematical Reviews number (MathSciNet)
MR116401

Zentralblatt MATH identifier
0249.62050

JSTOR
Ito, Koichi. Asymptotic Formulae for the Distribution of Hotelling's Generalized $T_0^2$ Statistic. II. Ann. Math. Statist. 31 (1960), no. 4, 1148--1153. doi:10.1214/aoms/1177705685. https://projecteuclid.org/euclid.aoms/1177705685