Multinomial model for random sums

In this paper, we study random sums relaxing the classical assumption of mutual independence between the variables involved. The possible dependence is measured by the correlation coefficient. We assume that the variables are assigned to independent clusters with equal correlation between them within the cluster. The multinomial distribution is an appropriate to model such a situation. As an application, we obtain the distribution of the accumulated claim for the reinsurer. A simulation study is performed and estimation of the parameters in the case of two clusters is presented.