The Generalized Poisson Count Technique and its Statistical Inference

Based on the Generalized Poisson distribution, the Generalized Poisson Count Technique is introduced to solve the over-dispersion and under-dispersion in the Poisson Item Count Technique. For the statistical inference, the iterative algorithm using EM algorithm and MM algorithm is studied to calculate the maximum likelihood estimate in the model by introducing the missing data and constructing the substitution function. Furthermore, in the simulation, the bias of the estimate is presented and the simulation results are discussed to find effective information.