Authors

• K. Nisa ¹
• C. C. Kokonendji ²
• A. Saefuddin ³

¹ Lampung University, Bandar Lampung, Indonesia.

² University of Franche-Comté, Besancon, France.

³ Bogor Agricultural University, Bogor, Indonesia.

Abstract

‎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.

Keywords

• Generalized variance
• Infinitely divisible measure
• Monge-Ampère equation
• Multivariate exponential family
• Variance function