Selecting the best statistical distribution to estimate the regression equation of traffic accidents with practical application

A thesis

Submitted to College of Administration and Economic-Karbala
University in partial fulfillment of the Requirements for the Degree
of master of Science in statistics
By

AbdulAmir Taaimeh Bandar AL-Salhi

Under supervision

A. Dr . Abdul hussian. H . HABEAB . AL-Tai

traffic accidents are an accident that occurs without prior planning by one vehicle and more than one vehicle. The accident may be with objects on the traffic or with an animal or an establishment It is important that before conducting any study of these incidents, it is necessary to know the statistical distribution suitable for them. This The thesis included three statistical distributions that will follow the data taken by each one, based on the comparison between the mean of these data and their variance, The study sample included the number of traffic accidents in Dhi Qar Governorate in 2016. The number of incidents occurring in the governorate was taken on a weekly basis (n = 52) and by comparing the mean and the variance The data show that the sum of the variance on the arithmetic mean is equal to the correct one, ie, the data follows the Poisson distribution. For the purpose of estimating the Poisson regression equation, four different methods were used: the MLE method, the less absolute deviation method (LAD) ,The kernel method and LIU method, were used in three tests to determine the significance of the estimated models: the Likelihood Ratio and the F test. The other test is to determine the significance of the estimated parameters of the Wald test, and five criteria were used for the comparison between the estimated models and the criteria are the Akaike, the BIC, the hanan quein (HQ), the (R^2), The latter is the mean squares error (MSE), By comparing the models estimated by these criteria, Liu method and the kernel regression method are better than the two methods maximun likelihood and less absolute deviations.