A definition of the coupled-product for multivariate coupled-exponentials

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 κd=κ/1+dκ, where d is the dimension 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. •A generalized product is defined to factor multivariate coupled exponentials.•The coupling is defined independent of the power and dimensions of the variable.•The output dimension of the generalized product is the sum of the input dimensions.