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This paper proposes an alternative bivariate negative binomial model based on the Sarmanov family, which is a more general tool than the existing bivariate negative binomial models, such as Marshall, Olkin (1990), in the sense it allows the heterogeneous dispersions and negative correlation between two dependent variables. We also expand the proposed bivariate negative binomial distribution to a regression model. The maximum likelihood estimators for parameters in the proposed model can be easily obtained by the conventional iterative methods like Fisher's scoring algorithm, which is another advantage of our proposal. We apply it to the data of the 1987-1988 National Medical Expenditure Survey (NMES) given by Deb, Trivedi (1997). The empirical result suggests that the proposed model has a performance better than the other bivariate negative binomial model of Marshall, Olkin (1990) in terms of the likelihood and the Akaike information criterion. Furthermore, our proposal can be easily extended to the modeling of bivariate zero inflated count data.
