# Analysis of the Railway Accident-Related Damages in South Korea
## 2 State of Art Statistical Models  
With respect to the statistical accident modeling efforts, some models were developed earlier for predicting accidents, based on a multiple linear regression model [10]. Since then, the statistical models applied to railway accident prediction have become more sophisticated by introducing categorical data analysis along with accident severity data in the form of logistics. [PERSON] et al. [5] developed a generalized logit model to determine the categorical characteristics of accident severity on railroad grade crossing. Different levels of injuries in accidents are modeled by either ordered logit or probit models [11; 12; 13]. By comparing various logit model structures such as the ordered probit, the multinomial logit and the random parameter logit model, [PERSON] and [PERSON] [14] showed that the random parameter logit model was the most suitable to evaluate the severities of injuries in railway level crossing accidents. Due to the random, discrete and non-negative nature of accident data, the models such as the Poisson regression model and the negative-binomial regression models [4] were widely used, instead of the linear regression models. However, the two heterogeneous distributions of measurements (for example, zero or positive) of accident data have not properly been explained by any classical models. In order to handle the excessive frequencies of zero in railway accident data, with no injuries and fatalities, the two-part models (TPMs) emerged as a solution, which consists of a degenerate distribution at zero and a non-zero distribution otherwise. Until now, a few studies suggested a zero-inflated negative-binomial and the zero-inflated Poisson model [15; 16; 17]. According to the non-zero distribution of a random component (or dependent variable), TPMs are of two types; 1) zero-inflated regression models for non-negative count data and 2) zero-inflated regression models for semi-continuous data; for example, zero-inflated Poisson model (ZIP) and zero-inflated negative-binomial model (ZINB) belong to the former type and zero-inflated gamma regression model (ZIG) and zero-inflated log-normal model (ZILN) belong to the latter type. There has been a lot of research on the two-part models. [PERSON] [18] applied ZIP to predict the number of defects in manufacturing. [PERSON] et al. [19] reviewed contemporary statistical models for count data with excessive zeros. [PERSON] and [PERSON] [20] compared generalized Poisson models with ZINB. [PERSON] et al. [21] contributed to significant correction for misclassification in caries research by using ZINB. [PERSON] et al. [22] proposed a Bayesian model for zero-inflated count data with an analysis of the psychiatric outpatient service use. [PERSON] et al. (2018) summarized TPMs for non-negative count measurements and semi-continuous data. [PERSON] and [PERSON] (2018) considered ZIG to analyze health care costs including a large proportion of \(\$0\) data. [PERSON] et al. (2018) analyzed time spent on leisure time physical activity using ZIG. [PERSON] et al. (2018) applied ZILN for the Prosopis caldenia pod production data at tree level in the Argentinean semiarid pampas. [PERSON] et al. (2018) suggest a zero-adjusted gamma model for mortgage loan loss given default contained extensive numbers of zeroes. [PERSON] et al. (2018) employed ZIP model with spatial effects to examine emergency department visits. [PERSON] et al. (2018) proposed the Bayesian modeling approach for fitting zero-inflated regression model. Bayesian approaches for modeling semi-continuous data are proposed by References (2018; 2018; 2018). This study proposes a new approach for evaluating the damages resulting from railway accidents using the TPMs such as the ZIP model and the ZINB model for the non-negative count measurements and the ZIG model and the ZILN model for the semi-continuous measurements. These models consist of a degenerate distribution at zero and a non-zero distribution using railway accident data.