A multivariate Poisson model based on a triangular comonotonic shock construction

Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling assumptions adequately reflect both the marginal behaviour and the associations between components. This article focuses specifically on developing a new multivariate Poisson model appropriate for multi-dimensional count data. The proposed formulation is based on convolutions of comonotonic shock vectors with Poisson-distributed components and allows for flexibility in capturing different degrees of positive dependence. In this article, we will present the general model framework along with various distributional properties. Several estimation techniques will be explored and assessed both through simulations and in a real data application involving extreme rainfall events.