The authors have provided an excellent and readable review of the Negative Binominal Distribution (NBD) model and how various violations of its assumptions may impact inferences which may be drawn from the model. They provide a theory of the sourced of bias and the qualitative impact of these bias sources - especially the issues of regularity, a spike at zero, and nonstationarity. Their presentation suggests that compensating errors from different sources of bias may account in large measure for the relative robustness (both in fit and in durability of use) of the NBD specification.
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