Equivalence of Partial and Conditional Correlation Coefficients

Abstract

Some classes of multivariate distributions, which have the same partial and conditional correlation coefficients, are obtained. In one class, the sum of components is fixed and all the components have negative correlation coefficients. Another class is constructed as mixtures of independent samples from the NEF-QVF mixed by conjugate prior, and all the components are positively correlated. Implications of the equivalence of partial and conditional covariances, and simple covariance structures are briefly discussed.