A two-parameter general inflated Poisson distribution: Properties and applications

•A new two-parameter general inflated Poisson distribution is proposed and studied.•The proposed model can be effectively used for fitting underdispersed and overdispersed count data.•A general mechanism for inflating the zero and non-zero values of any discrete distribution is offered.•Real-data examples illustrate the practical usefulness of the proposed model.

In this work, we propose and study a two-parameter modification of the ordinary Poisson distribution that is suitable for the modeling of non-typical count data. This model can be viewed as an extension of the zero-inflated Poisson distribution. We derive the proposed model as a special case of a general one and focus our study on it. The theoretical properties for each model are given, while estimation methods for the two-parameter model are discussed as well. Three practical examples illustrate its usefulness. The results show that the proposed model is very flexible in the modeling of various types of count data.