An one-parameter compounding discrete distribution.

In this study, a new one-parameter discrete distribution obtained by compounding the Poisson and xgamma distributions is proposed. Some statistical properties of the new distribution are obtained including moments and probability and moment generating functions. Two methods are used for the estimation of the unknown parameter: the maximum likelihood method and the method of moments. Additionally, the count regression model and integer-valued autoregressive process of the proposed distribution are introduced. Some possible applications of the introduced models are considered and discussed.