Bayesian Estimation for {ij}-Inflated Mixture Power Series Distributions using an EM Algorithm

The purpose of this article was to illustrate how we can model different behaviors of subpopulations by introducing a mixing distribution/regression model with {ij}-inflated power series. An EM algorithm was used to estimate the parameters of the models. As a practical application, the new model has been applied to the design of an optimal rate-making system. More precisely, this article employs a number of reported claims from an Iranian third party insurance dataset, under an {ij}inflated power series mixture distribution/regression model to estimate rate premium for such insurance contract. The numerical study shows that the {ij}-inflated negative Binomial mixture models have the potential to provide more appropriate rate premiums for policyholders under a rate-making system with four categories.