## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 39, Number 1 (1968), 227-232.

### On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta Distributions

#### Abstract

Of several possible versions of multiple correlation matrix between two sets of variables $\mathbf{x}$ and $\mathbf{y}$ (see, e.g., Khatri, 1964), we derive using the techniques of A. T. James (zonal polynomials), the non-null distribution of one version when (i) one of the two sets of variables is fixed, i.e., multivariate analysis of variance and covariance case (MANOVA), and when (ii) both sets of variables are random variables, i.e., canonical correlations case. These distributions are non-central multivariate $\beta$-distributions in much the same way as the two cases of multiple correlation commonly known as the multiple correlation of the second and the first kind respectively.

#### Article information

**Source**

Ann. Math. Statist., Volume 39, Number 1 (1968), 227-232.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177698522

**Digital Object Identifier**

doi:10.1214/aoms/1177698522

**Mathematical Reviews number (MathSciNet)**

MR219186

**Zentralblatt MATH identifier**

0174.22905

**JSTOR**

links.jstor.org

#### Citation

Srivastava, M. S. On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta Distributions. Ann. Math. Statist. 39 (1968), no. 1, 227--232. doi:10.1214/aoms/1177698522. https://projecteuclid.org/euclid.aoms/1177698522

#### Corrections

- See Correction: M. S. Srivastava. Correction Notes: Correction to "On the Distribution of a Multiple Correlation Matrix: Non-Central Multivariate Beta-Distributions". Ann. Math. Statist., Volume 39, Number 4 (1968), 1359--1359.Project Euclid: euclid.aoms/1177698266