;Zero-inflated generalized Poisson distribution and zero inflated negative binomial distribution are models proposed for analyzing over-dispersed count data with excess zeros. We illustrate that inferences derived from these models are sensitive to model misspecification. Alternatively, we show that one can fix the normal model to accommodate data with the features of interest. The adjusted normal likelihood is asymptotically legitimate so long as the first two moments are correctly specified and that the 3rd and the 4th moments of the true distributions exist.
