A common zero-inflation bivariate Poisson model with comonotonic and counter-monotonic shocks

There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate data, characterizing an appropriate dependence structure is equally critical in order to adequately assess the underlying risk inherent in the joint counts. In this work we propose a new bivariate zero-inflated Poisson model appropriate for modeling pairs of counts with a surplus of zeros. The proposed construction is based on a mixture model involving a common mass at zero along with a Poisson random pair. Various forms of dependence are considered for the latent Poisson pair, allowing for both negative and positive dependence. Several model properties are explored, notably the joint probability mass function and implied dependence structure. The method of moments and maximum likelihood approaches are described and implemented for estimation. The usual asymptotic properties of the estimators are derived, and their finite sample properties are explored through extensive simulations. The practical use of the proposed model is further illustrated through two real data applications.