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.
Highlights
The correlation matrix plays an important role in multivariate analysis since by itself it captures the pairwise degrees of relationship between different components of a random vector
Component Analysis and Factor Analysis, where in general, it gives results different from those obtained with the covariance matrix
The distribution of the sample correlation matrix R is relatively easy to compute, and its determinant has a distribution that can be expressed as a Meijer G-function distribution
Summary
The correlation matrix plays an important role in multivariate analysis since by itself it captures the pairwise degrees of relationship between different components of a random vector. Component Analysis and Factor Analysis, where in general, it gives results different from those obtained with the covariance matrix. The distribution of the sample correlation matrix R is relatively easy to compute, and its determinant has a distribution that can be expressed as a Meijer G-function distribution. When Λ ≠ I no expression for the density of R is presently available in the literature, and the distribution of its determinant is still unknown, in spite of efforts made by several researchers. We will provide here the closed form expression of the distribution of R, with the sample variances as parameters, complementing a result presented by Fisher in [2]
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.