 2010 The Author. Journal compilation  2010 VVS. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. doi:10.1111/j.1467-9574.2009.00446.x 112 Statistica Neerlandica (2010) Vol. 64, nr. 1, pp. 112–124 A new bivariate generalized Poisson distribution Felix Famoye* Department of Mathematics, Central Michigan University, Mt Pleasant, MI 48859, USA In this paper, a new bivariate generalized Poisson distribution (GPD) that allows any type of correlation is defined and studied. The marginal distributions of the bivariate model are the univariate GPDs. The parameters of the bivariate distribution are estimated by using the moment and maximum likelihood methods. Some test statistics are discussed and one numerical data set is used to illustrate the applications of the bivariate model. Keywords and Phrases: correlated count data, over- and under- dispersion, score test, estimation. 1 Introduction The Poisson distribution has been used to model the number of rare events that occur in time, area, region, volume or space. Examples include the number of births over a time period, number of typing errors per page, number of telephone calls per hours received by an office, number of faults in rolls of fabric, the number of auto- mobile accidents, home injuries and industrial accidents over a given unit of time. Biological applications include using the Poisson distribution to model the number of fish caught over a time period, number of bacteria counts over an area and number of bugs per leaf. The distribution has been used in many areas of study including medicine, engineering, insurance, marketing, social sciences and education (for example, see Cameron and Trivedi 1998; Winkelmann, 2008). The Poisson model assumes that events occur under the principle of complete randomness. There are several examples where this principle does not hold. For example, insects that lay eggs to produce offspring may tend to lay eggs in areas with eggs leading to overcrowding or lay eggs in areas with no eggs. This depends on the social behavior of the insects. Feelings of social association are strong in some insects while it is weak in other insects. The Poisson model, characterized by one parameter, has its mean equal to the variance. As the mean and variance of the Poisson distribution are equal, we say that the Poisson distribution satisfies the equi-dispersion property. This property is often violated in real-life count data. *felix.famoye@cmich.edu