Characterizations of Multivariate Normal-Poisson Model

Multivariate normal-poisson model has been recently introduced as a special case of normal stable tweedie models. the model is composed of a univariate poisson variable, and the remaining variables given the poisson one are independent gaussian variables with variance the value of the poisson component. two characterizations of this model are shown, first by variance function and then by generalized variance function which is the determinant of the variance function. the latter provides an explicit solution of a particular monge-ampère equation.