Extending normal gamma and normal inverse Gaussian models, multivariate normal stable Tweedie (NST) models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of multivariate exponential families, the NST models are recently classified by their covariance matrices V(m) depending on the mean vector m. In this paper, we prove the characterization of all the NST models through their determinants of V(m), also called generalized variance functions, which are power of only one component of m. This result is established under the NST assumptions of Monge-Ampère property and steepness. It completes the two special cases of NST, namely normal Poisson and normal gamma models. As a matter of fact, it provides explicit solutions of particular Monge-Ampère equations in differential geometry.

扩展正态伽马和正态高斯逆模型，多元正态稳定Tweedie（NST）模型由具有正值域的固定单变量稳定Tweedie变量组成，给定的其余随机变量是具有相同方差的真实独立高斯变量等于固定分量。在多元指数族的框架内，NST模型最近根据均值向量m通过协方差矩阵V（m）进行分类。在本文中，我们通过N（V）的行列式（也称为广义方差函数）证明了所有NST模型的特征，它们仅是m的一个分量的幂。该结果是在NST对Monge-Ampère属性和陡度的假设下建立的。它完成了NST的两种特殊情况，即普通泊松模型和普通伽玛模型。实际上，它为微分几何中的特定Monge-Ampère方程提供了明确的解决方案。