Modeling over-dispersed crash data with a long tail: Examining the accuracy of the dispersion parameter in Negative Binomial models

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Exploring the application of the negative binomial-generalized exponential model for analyzing traffic crash data with excess zeros (2015, methodology): “…2012; Hallmark et al., 2013; Xu and Sun, 2015), the Poisson-weighted exponential model (Zamani et al., 2014), the Poisson Inverse Gaussian (PIG) (Zha et al., 2015), the Negative Binomial-Crack (NBCR) distribution (Saengthong and Bodhisuwan, 2013), and the Sichel (SI) model (Zou et al., 2013; 2015).”
Random parameters multivariate tobit and zero-inflated count data models: addressing unobserved and zero-state heterogeneity in accident injury-severity rate and frequency analysis (2016, background): “injuries, and fatalities are modeled simultaneously, overdispersion is expected (Shankar et al., 1998; 179 Venkataraman et al., 2014; Zou et al., 2015).”
Developing a Random Parameters Negative Binomial-Lindley Model to analyze highly over-dispersed crash count data (2018, background): “However, recent studies have pointed out that with a heavy-tailed crash dataset, the NB model can produce biased parameter estimates (Zou et al. 2015, Shirazi et al. 2016).”