Multiple arbitrarily inflated Poisson regression analysis

In this paper, a new flexible count regression analysis is proposed. For this purpose, a new modification of the Poisson distribution is introduced which generalizes the Poisson, zero-inflated Poisson, zero-one inflated Poisson, and zero-one-two inflated Poisson distributions. Some distributional properties are discussed for the proposed distribution. The Fisher scoring and EM algorithms are derived to attain the maximum likelihood estimates of the unknown parameters. An expected Fisher information matrix is provided to construct an approximate confidence interval for the parameters. Using the modified Poisson distribution, an arbitrary multiply inflated counting regression model is proposed. The performance of the maximum likelihood methodology is investigated with a simulation study for the distribution and count regression model. Finally, two practical data sets are analyzed and the superiority of the proposed model is demonstrated among others.