Seemingly Unrelated Negative Binomial Regression

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Multivariate Negative Binomial Models for Insurance Claim Counts (2014, background): “The NB-I model implies a constant dispersion ϕ = 1 + σ2, while the NB-II model allows for subject heterogeneity in the dispersion ϕ = 1 + σ2 exp(x ′ β) (see Winkelmann (2008)).”
Regression in a copula model for bivariate count data (2010, methodology): “Examples are the bivariate Poisson distribution, described in detail by Kocherlakota and Kocherlakota [16] and its generalizations, based usually on mixtures as described in Aitchinson and Ho [1], Winkelmann [31], Chib and Winkelmann [5], Karlis and Xekalaki [15].”