Abstract
In this article, we compare the zero-inflated Poisson (ZIP) and negative binomial (NB) distributions based on three most important criteria: the probability of zero, the mean value, and the variance. Our results show that with same mean value and variance, the ZIP distribution always has a larger probability of zeros; with same mean value and probability of zeros, the NB distribution always has a larger variance; and with same variance and probability of zeros, the ZIP distribution always has a larger mean value. We also study the properties of Vuong test in model selection in three cases by simulations.
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