Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a...Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are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
Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the predict...Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the prediction of the number of crashes that would occur on a specific road segment or intersection in a time period, while crash severity models generally explore the relationship between crash severity injury and the contributing factors such as driver behavior, vehicle characteristics, roadway geometry, and road-environment conditions. Effective interventions to reduce crash toll include design of safer infrastructure and incorporation of road safety features into land-use and transportation planning;improvement of vehicle safety features;improvement of post-crash care for victims of road crashes;and improvement of driver behavior, such as setting and enforcing laws relating to key risk factors, and raising public awareness. Despite the great efforts that transportation agencies put into preventive measures, the annual number of traffic crashes has not yet significantly decreased. For in-stance, 35,092 traffic fatalities were recorded in the US in 2015, an increase of 7.2% as compared to the previous year. With such a trend, this paper presents an overview of road crash prediction models used by transportation agencies and researchers to gain a better understanding of the techniques used in predicting road accidents and the risk factors that contribute to crash occurrence.展开更多
In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial ...In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.展开更多
文摘Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
文摘Background： In this paper, a regression model for predicting the spatial distribution of forest cockchafer larvae in the Hessian Ried region （Germany） is presented. The forest cockchafer, a native biotic pest, is a major cause of damage in forests in this region particularly during the regeneration phase. The model developed in this study is based on a systematic sample inventory of forest cockchafer larvae by excavation across the Hessian Ried. These forest cockchafer larvae data were characterized by excess zeros and overdispersion. Methods： Using specific generalized additive regression models, different discrete distributions, including the Poisson, negative binomial and zero-inflated Poisson distributions, were compared. The methodology employed allowed the simultaneous estimation of non-linear model effects of causal covariates and, to account for spatial autocorrelation, of a 2-dimensional spatial trend function. In the validation of the models, both the Akaike information criterion （AIC） and more detailed graphical procedures based on randomized quantile residuals were used. Results： The negative binomial distribution was superior to the Poisson and the zero-inflated Poisson distributions, providing a near perfect fit to the data, which was proven in an extensive validation process. The causal predictors found to affect the density of larvae significantly were distance to water table and percentage of pure clay layer in the soil to a depth of I m. Model predictions showed that larva density increased with an increase in distance to the water table up to almost 4 m, after which it remained constant, and with a reduction in the percentage of pure clay layer. However this latter correlation was weak and requires further investigation. The 2-dimensional trend function indicated a strong spatial effect, and thus explained by far the highest proportion of variation in larva density. Conclusions： As such the model can be used to support forest practitioners in their decision making for regeneration and forest protection planning in the Hessian predicting future spatial patterns of the larva density is still comparatively weak. Ried. However, the application of the model for somewhat limited because the causal effects are
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.
文摘Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the prediction of the number of crashes that would occur on a specific road segment or intersection in a time period, while crash severity models generally explore the relationship between crash severity injury and the contributing factors such as driver behavior, vehicle characteristics, roadway geometry, and road-environment conditions. Effective interventions to reduce crash toll include design of safer infrastructure and incorporation of road safety features into land-use and transportation planning;improvement of vehicle safety features;improvement of post-crash care for victims of road crashes;and improvement of driver behavior, such as setting and enforcing laws relating to key risk factors, and raising public awareness. Despite the great efforts that transportation agencies put into preventive measures, the annual number of traffic crashes has not yet significantly decreased. For in-stance, 35,092 traffic fatalities were recorded in the US in 2015, an increase of 7.2% as compared to the previous year. With such a trend, this paper presents an overview of road crash prediction models used by transportation agencies and researchers to gain a better understanding of the techniques used in predicting road accidents and the risk factors that contribute to crash occurrence.
基金supported by National Natural Science Foundation of China(Nos.11871027,11731015)Science and Technology Developing Plan of Jilin Province(No.20170101057JC)Cultivation Plan for Excellent Young Scholar Candidates of Jilin University.
文摘In this paper,we study a robust estimation method for the observation-driven integervalued time-series models in which the conditional probability mass of current observations is assumed to follow a negative binomial distribution.Maximum likelihood estimator is highly affected by the outliers.We resort to the minimum density power divergence estimator as a robust estimator and showthat it is strongly consistent and asymptotically normal under some regularity conditions.Simulation results are provided to illustrate the performance of the estimator.An application is performed on data for campylobacteriosis infections.
