A new multivariate Poisson model

TL;DR

This paper introduces a flexible multivariate Poisson model for multi-dimensional count data, capturing positive dependence, with methods for estimation demonstrated through simulations and rainfall data analysis.

Contribution

It presents a novel multivariate Poisson model based on convolutions of comonotonic shocks, enhancing modeling of dependencies in count data.

Findings

Model effectively captures positive dependence.

Estimation methods perform well in simulations.

Application to rainfall data demonstrates practical utility.

Abstract

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.