PURPOSES: The purpose of this study is to develop a crash prediction model at signalized intersections, which can capture the randomness and uncertainty of traffic accident forecasting in order to provide more precise results. METHODS: The authors propose a random parameter (RP) approach to overcome the limitation of the Count model that cannot consider the heterogeneity of the assigned locations or road sections. For the model’s development, 55 intersections located in the Daejeon metropolitan area were selected as the scope of the study, and panel data such as the number of crashes, traffic volume, and intersection geometry at each intersection were collected for the analysis. RESULTS: Based on the results of the RP negative binomial crash prediction model developed in this study, it was found that the independent variables such as the log form of average annual traffic volume, presence or absence of left-turn lanes on major roads, presence or absence of right-turn lanes on minor roads, and the number of crosswalks were statistically significant random parameters, and this showed that the variables have a heterogeneous influence on individual intersections. CONCLUSIONS : It was found that the RP model had a better fit to the data than the fixed parameters (FP) model since the RP model reflects the heterogeneity of the individual observations and captures the inconsistent and biased effects.

PURPOSES : The objective was to develop the advanced method which could not explain each observation’s specific characteristic in the present negative binomial method that results in under-estimation of the standard error(t-value inflation) and affects the confidence of whole derived results. METHODS : This study dealt with traffic accidents occurring within interchange segment on highway main line with RPNB(Random Parameter Negative Binomial) method that enables to take account of heterogeneity. RESULTS : As a result, AADT and lighting installation type on the road were revealed to have random parameter and in terms of other geometric variables, all were derived as fixed parameter(same effect on every segment). Also, marginal effects were adapted to analyze the relative effects on traffic accidents. CONCLUSIONS : This study proves that RPNB method which considers each observation’s specific characteristics is better fitted to the accident data with geometrics. Thus, it is recommended that RPNB model or other methods which could consider the heterogeneity needs to be adapted in accident analysis.

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application.

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application.

Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application. We here assume that customer order sizes are described by the Poisson distribution with the random parameter following a gamma distribution. This implies in turn that the negative binomial distribution is obtained by mixing the mean of the Poisson distribution with a gamma distribution. The purpose of this paper is to give an interpretation of the negative binomial demand process by considering the sources of variability in the unknown Poisson parameter. Such variability comes from the unknown demand rate and the unknown lead time interval.