On the Small Count Inflated Poisson Distribution

Inflated count distributions are used in situations where counts of an underlying distribution of a population are larger than expected by traditional count distributions. One of the most commonly used inflated count distributions is the zero-inflated Poisson distribution. This work demonstrates the construction of a small count inflated Poisson distribution, of which the zero-inflated Poisson distribution is a special case. Model construction and parameter estimation are shown. Simulations analyzing asymptotic properties, group prediction, and count prediction are presented. Conclusions and recommendations for future research are discussed