The extra zeros in traffic accident data: a study on the mixture of discrete distributions

Abstract

The presence of extra zeros is commonly observed in traffic accident count data. Past research opt to the zero altered models and explain that the zeros are sourced from under reporting situation. However, there is also an argument against this statement since the zeros could be sourced from Poisson trial process. Motivated by the argument, we explore the possibility of mixing several discrete distributions that can contribute to the presence of extra zeros. Four simulation studies were conducted based on two accident scenarios and two discrete distributions: Poisson and negative binomial; by considering six combinations of proportion values correspond to low, moderate and high mean values in the distribution. The results of the simulation studies concur with the claim as the presence of extra zeros is detected in most cases of mixed Poisson and mixed negative binomial data. Data sets that are dominated by Poisson (or negative binomial) with low mean show an apparent existence of extra zeros although the sample size is only 30. An illustration using a real data set concur the same findings. Hence, it is essential to consider the mixed discrete distributions as potential distributions when dealing with count data with extra zeros. This study contributes on creating awareness of the possible alternative distributions for count data with extra zeros especially in traffic accident applications.