Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we...Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we propose a more flexible integer-valued GARCH model based on the generalized Conway-Maxwell-Poisson distribution to model time series of counts,which offers a unified framework to deal with overdispersed or underdispersed,zero-inflated and heavy-tailed time series of counts.This distribution generalizes the Conway-Maxwell-Poisson distribution by adding a parameter,which plays the role of controlling the length of the tail.We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method.The numerical results with both simulated and real data confirm the good performance of the proposed model.展开更多
This paper presents the ZINDOT model,a methodology utilizing a zero-inflated negative binomial model with the variables used in the United States Department of Transportation(USDOT)accident prediction formula,to deter...This paper presents the ZINDOT model,a methodology utilizing a zero-inflated negative binomial model with the variables used in the United States Department of Transportation(USDOT)accident prediction formula,to determine the expected accident count at a highway-rail grade crossing.The model developed contains separate formulas to estimate the crash prediction value depending on the warning device type installed at the crossing:crossings with gates,crossings with flashing lights and no gates,and crossings with crossbucks.The proposed methodology also accounts for the observed accident count at a crossing using the Empirical Bayes method.The ZINDOT model estimates were compared to the USDOT model estimates to rank the crossings based on the expected accident frequency.It is observed that the new model can identify crossings with a greater number of accidents with Gates and Flashing Lights and Crossbucks in both Illinois(data which were used to develop the model)and Texas(data which were used to validate the model).A practitioner already using the USDOT formulae to estimate expected accident count at a crossing could easily use the ZINDOT model as it employs the same variables used in the USDOT formula.This methodology could be used to rank highway-rail grade crossings for resource allocation and safety improvement.展开更多
基金the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Teacher’s Research Support Project Foundation of Jiangsu Normal University(No.21XFRS022)National Natural Science Foundation of China(Nos.12271206,11871027)Natural Science Foundation of Jilin Province(No.20210101143JC).
文摘Time series of counts observed in practice often exhibit overdispersion or underdispersion,zero inflation and even heavy-tailedness(the tail probabilities are non-negligible or decrease very slowly).In this article,we propose a more flexible integer-valued GARCH model based on the generalized Conway-Maxwell-Poisson distribution to model time series of counts,which offers a unified framework to deal with overdispersed or underdispersed,zero-inflated and heavy-tailed time series of counts.This distribution generalizes the Conway-Maxwell-Poisson distribution by adding a parameter,which plays the role of controlling the length of the tail.We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method.The numerical results with both simulated and real data confirm the good performance of the proposed model.
文摘This paper presents the ZINDOT model,a methodology utilizing a zero-inflated negative binomial model with the variables used in the United States Department of Transportation(USDOT)accident prediction formula,to determine the expected accident count at a highway-rail grade crossing.The model developed contains separate formulas to estimate the crash prediction value depending on the warning device type installed at the crossing:crossings with gates,crossings with flashing lights and no gates,and crossings with crossbucks.The proposed methodology also accounts for the observed accident count at a crossing using the Empirical Bayes method.The ZINDOT model estimates were compared to the USDOT model estimates to rank the crossings based on the expected accident frequency.It is observed that the new model can identify crossings with a greater number of accidents with Gates and Flashing Lights and Crossbucks in both Illinois(data which were used to develop the model)and Texas(data which were used to validate the model).A practitioner already using the USDOT formulae to estimate expected accident count at a crossing could easily use the ZINDOT model as it employs the same variables used in the USDOT formula.This methodology could be used to rank highway-rail grade crossings for resource allocation and safety improvement.
