M-Matrices as covariance matrices of multinormal distributions

The class of multivariate normal densities n(0, Σ) whose inverse covariance matrix Σ)^-1 is an M-matrix is equivalent to this normal density being multivariate totally positive of order 2(MTP₂). Equivalent characterizations are given in terms of certain partial correlation coefficients being positive. It is further shown that related partial and multiple regression coefficients and canonical correlation are positive. When Σ is an M-matrix the corresponding normal random vector components are negatively associated. This concept and some extensions are discussed.