  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 behavior as well as the
associations between components. This work 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 paper, the general model
framework will be presented 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.
