ScholarLens Back to search
1971•The Annals of Mathematical StatisticsOpen access

A Characterization of the Multivariate Normal Distribution

Mary R. Anderson

Open full text 8 citations

Abstract

In this paper we characterize the multivariate normal distribution through the mean vector of the distribution. In Theorem 3, we find that the multivariate normal distribution can also be characterized through its variance, even though unknown, provided the variance-covariance matrix is free of the parameter involved. We are able to determine the mean vector to within two unknowns, the variance-covariance matrix and a constant vector.

Open-access reader

About this research paper

What this paper is about

In this paper we characterize the multivariate normal distribution through the mean vector of the distribution. In Theorem 3, we find that the multivariate normal distribution can also be characterized through its variance, even though unknown, provided the variance-covariance matrix is free of the parameter involved. We are able to determine the mean vector to within two unknowns, the variance-covariance matrix and a constant vector.

Why it matters

OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper we characterize the multivariate normal distribution through the mean vector of the distribution. In Theorem 3, we find that the multivariate normal distribution can also be characterized through its variance, even though unknown, provided the variance-covariance matrix is free of the parameter involved. We are able to determine the mean vector to within two unknowns, the variance-covariance matrix and a constant vector.

Key concepts: Matrix t-distribution, Mathematics, Normal-Wishart distribution, Multivariate normal distribution, Scatter matrix, Matrix normal distribution, Multivariate analysis of variance, Inverse-Wishart distribution

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A Characterization of the Multivariate Normal Distribution — Research Paper | ScholarLens