Characterizations of Multivariate Normal-Poisson Model

ýMultivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie modelsý. ýThe model is composed of a univariate Poisson variableý, ýand the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson componentý. ýTwo characterizations of this model are showný, ýfirst by variance function and then by generalized variance function which is the determinant of the variance functioný. ýThe latter provides an explicit solution of a particular Monge-Ampère equation.