A Doubly-Inflated Poisson Distribution and Regression Model

A doubly-inflated Poisson distribution is presented to account for count inflation at some positive integer value k in addition to that seen at zero. Maximum likelihood and moment estimators are derived, and their performances are compared using asymptotic relative efficiencies. The doubly-inflated Poisson distribution is also incorporated into the generalized linear models framework to account for associations with covariates in modeling the count mean as well as the probability of inflation.