Distributions of Hotelling'sT2and Multiple and Partial Correlation Coefficients for the Mixture of Two Multivariate Gaussian Populations
Arjun K. Gupta, D. G. Kabe · Statistics · 1999
For the mixture of two multivariate normal populations Srivastava and Awan (1982), and Srivastava (1983) derive the densities of Hotelling's-T 2, and the multiple correlation coefficient. They do not express their results in the standard forms available for a single multivariate normal population. In this paper we derive these distributions in the standard forms and also study the distribution of partial correlation coefficient. The results depend on the fact that the latent vectors of an identity matrix and of a projection idempotent matrix are the same.