Examing the Poisson-Weibull Generalized Model for Analyzing Crash Data
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Over the last 20 to 30 years, there have been a significant number of statistical methods proposed for analyzing crash data. Traffic crashes are characterized as random and independent discrete non-negative events. Crash data have often been shown to exhibit over-dispersion. Therefore, the Negative Binomial (NB) is the preferred and widely used model to analyze this kind of data. Although NB model is very popular in traffic safety area, it still has limitations modeling crash data especially when crash data are characterized by low sample mean and small sample size. The main research objective of this thesis is to develop a new statistical method namely, Poisson-Weibull (PW) Generalized Linear Model (GLM) to analyze vehicle crash data and to evaluate its modeling performance at different dispersion levels. This study makes use of both simulated and observed data for accomplishing the research objectives. The PW model is the mixture of Poisson and Weibull distributions. In this research, the statistical characteristics of the PW model were well defined and the parameters were estimated using a Bayesian approach. The PW model was initially evaluated using a series of simulated data for different dispersion levels. It was found that the PW model was able to reproduce and capture the true parameter values with high accuracy. After the initial analysis using the simulated data, the PW GLM was applied to two observed datasets and compared with the NB model. The goodness-of-fit (GOF) tests and model comparisons showed that the PW model performed as well as the NB model. Therefore, the PW model can be considered as an innovative and promising alternative for analyzing crash data.
Cheng, Lingzi (2012). Examing the Poisson-Weibull Generalized Model for Analyzing Crash Data. Master's thesis, Texas A&M University. Available electronically from