Distribution characteristics of traffic crash data of freeway based on statistics and hypothesis test

In order to analyze the distribution characteristics of traffic crash data on the basic sections of freeway, traffic crash number, fatal and injury crash number, death and injury numbers of traffic crash were taken as discrete random variables, and crash interval time and average annual crash number per kilometer were taken as continuous random variables. For discrete crash data, the sections of freeway were divided by using equally divided method, dynamic clustering method and sliding window method, and crash data were fitted by using Poisson distribution, negative binomial distribution, zero-inflated Poisson distribution and zero-inflated negative binomial distribution. For continuous crash data, the sections were divided based on the toll intervals, crash data were fitted by using normal distribution and negative exponential distribution. The goodness-of-fit tests of various fitting results were performed by using Pearson's square. Analysis result shows that in all sections, crash numbers are subject to negative binomial distribution, and in some cases, obey negative binomial distribution and Poisson distribution at the same time. Fatal and injury crash number and death number of traffic crash mainly obey zero-inflated Poisson distribution or zero-inflated negative binomial distribution. The probabilities of goodness-of-fit test are all greater than 0.05. Average annual crash number per kilometer is more subject to normal distribution, while crash interval time mainly obeys negative exponential distribution, and the probabilities of goodness-of-fit test are also greater than 0.05. The statistical distribution characteristic of traffic crash data is one of the prerequisites for establishing crash prediction model and the identification of crash black spots, and crash interval time can be used as the measurement indicator of safety reliability.