Distribution of the Sample Correlation Matrix and Applications

Thu Pham-Gia, Vartan Choulakian

Department of Mathematics and Statistics, Université de Moncton, Moncton, Canada.

DOI: 10.4236/ojs.2014.45033                

Abstract

For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as parameters. Also, the distribution of its determinant is established in terms of Meijer G-functions in the null-correlation case. Several numerical examples are given, and applications to the concept of system de- pendence in Reliability Theory are presented.

Keywords

Correlation, Normal, Determinant, Meijer G-Function, No-Correlation, Dependence, Component, Formatting, Style, Styling, Insert

Conflicts of Interest

The authors declare no conflicts of interest.

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