Negative Binomial-Generalized Exponential Distribution: Generalized Linear Model and its Applications

Abstract

Modelling crash data has been an integral part of the research done in highway safety. Different tools have been suggested by researchers to analyze crash data. One such tool, which was recently proposed, is the Negative Binomial Generalized Exponential (NB-GE) distribution. As the name suggests, it is a combination of Negative Binomial and Generalized Exponential distribution. This distribution has three parameters and can handle over-dispersed crash data which are characterized by a large number of zeros and/or long tail. This research seeks to develop a generalized linear model (GLM) for NB-GE distribution and discuss its applications in crash data analysis. The NB-GE GLM was applied to two over-dispersed crash datasets and its performance was compared to Negative Binomial-Lindley (NB-L) and Negative Binomial (NB) models using various statistical measures. It was found that NB-GE performs almost as well as NB-L model and performs much better than the NB model. This research tried to determine the percentage of zeroes and the dispersion in the dataset where the NB-GE model is recommended over the NB model for ranking sites. Datasets were simulated for different scenarios. It was found that for high dispersion the NB-GE model performs better than the NB model when the percentage of zero counts in the dataset is greater than 80%. When dataset has lower than 80% zeroes then NB model and NB-GE model perform similarly. Hence for lower percentages NB model would be preferred as it is simpler and easier to use.