The negative binomial–Lindley distribution as a tool for analyzing crash data characterized by a large amount of zeros

Abstract

The modeling of crash count data is a very important topic in highway safety. As documented in the literature, given the characteristics associated with crash data, transportation safety analysts have proposed a significant number of analysis tools, statistical methods and models for analyzing such data. Among the data issues, we find the one related to crash data which have a large amount of zeros and a long or heavy tail. It has been found that using this kind of dataset could lead to erroneous results or conclusions if the wrong statistical tools or methods are used. Thus, the purpose of this paper is to introduce a new distribution, known as the negative binomial-Lindley (NB-L), which has very recently been introduced for analyzing data characterized by a large number of zeros. The NB-L offers the advantage of being able to handle this kind of datasets, while still maintaining similar characteristics as the traditional negative binomial (NB). In other words, the NB-L is a two-parameter distribution and the long-term mean is never equal to zero. To examine this distribution, simulated and observed data were used. The results show that the NB-L can provide a better statistical fit than the traditional NB for datasets that contain a large amount of zeros.