  The coupled-product and coupled-exponential of the generalized calculus of
nonextensive statistical mechanics are defined for multivariate functions. The
nonlinear statistical coupling is indexed such that k_d = k/(1+dk), where d is
the dimensions of the argument of the multivariate coupled-exponential. The
coupled-Gaussian distribution is defined such that the argument of the
coupled-exponential depends on the coupled-moments but not the coupling
parameter. The multivariate version of the coupled-product is defined such that
the output dimensions are the sum of the input dimensions. This enables
construction of the multivariate coupled-Gaussian from univariate
coupled-Gaussians. The resulting construction forms a model of coupling between
distributions, generalizing the product of independent Gaussians.
