Discrete distributions when modeling the disability severity score of motor victims

Boucher, Jean‐Philippe; Santolino, Miguel

doi:10.1016/j.aap.2010.06.015

Cited by 25 publications

(14 citation statements)

References 50 publications

(35 reference statements)

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“…According to them, the claim is made that zero-inflated models assume two sources of zeros: "true" and "observed". The existence of "true" zeros may be too strong an assumption in some cases (see also Boucher and Santolino (2010)). However, as Park and Lord (2009) discuss in the univariate case, the two-component mixture model used here does not make this somewhat strict dual-state process assumption and allows mixing with respect to both zeros and positives.…”

Section: Resultsmentioning

confidence: 99%

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Bermúdez

Karlis

2012

Computational Statistics & Data Analysis

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Bivariate Poisson regression models for ratemaking in car insurance has been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, it is shown that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Finally, an EM algorithm is provided in order to ensure the models' ease-offit. These models are applied to an automobile insurance claims data set and it is shown that the modelling of the data set can be improved considerably.

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Section: Resultsmentioning

confidence: 99%

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Bermúdez

Karlis

2012

Computational Statistics & Data Analysis

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“…However, the negative coefficient in the second-layer hurdle model indicates that, conditional on a positive crash rate, a road segment with more than two lanes is inclined to have a lower crash rate. Such a situation of coefficient confliction can happen if the models have more than one set of coefficients, for example, zero-inflated models (e.g., [16]) and hurdle models (e.g., [27]). Counterintuitive signs were also mentioned in the study of Shankar et al [16].…”

Section: Hurdle Models Using Different Distributions For Positive Cramentioning

confidence: 99%

Modeling traffic crash rates of road segments through a lognormal hurdle framework with flexible scale parameter

Yan

Weng

2015

J of Advced Transportation

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SUMMARYThis study examines distributional characteristics of crash rates for road segments using observed accident data. The results indicate that the distribution of crash rates is mixed and right-skewed, which motivates the consideration of non-normal distributions. With the aid of Kolmogorov-Smirnov tests, kernel density plots, and Q-Q plots, the lognormal distribution is verified as an appropriate candidate for representing the positive domain of crash rates. Then, a lognormal hurdle model was developed and also compared with gamma and Weibull hurdle models. Further, the lognormal hurdle model was revised by allowing the scale parameter to vary with respect to explanatory variables. Such a modification enables the heterogeneous skewness of samples to be captured while enhancing the modeling flexibility. The proposed model was also compared with a Tobit model, an alternative approach that treats crash rates as censored data. Among all these models, the proposed lognormal hurdle model with flexible scale parameter presents the best modeling performance, and the analyses also reveal that several explanatory variables affect crash rates through not only the location parameter but also the scale parameter in the lognormal model. This study finally attempted to inspect crash rates through count models, and it discovered that the proposed hurdle model is superior because it is able to output the whole distribution form of crash rates, whereas the crash count model can only provide the expected value of crash rates, provided the exposure variable servers as an offset term in the link function of the mean parameter.

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“…Many crash severity studies have found that females involved in motor collisions suffer more serious injuries than do males (Rifaat and Tay, 2009;Evans, 2001;Kockelman and Kweon, 2002), whereas other authors suggest that males are involved in more serious crashes (Tay and Rifaat, 2007;Valent et al, 2002). The extant literature indicates that the victim's age positively influences the frequency and severity of injuries (O'Donnell and Connor, 1996;Delen et al, 2006;Boucher and Santolino, 2010), although some studies have found a nonlinear relationship between age and severity (Newgard, 2008). Regarding the type of victim, a distinction is made between driver, passenger and non-motorized road user.…”

Section: Spanish Databasementioning

confidence: 99%

Factors affecting hospital admission and recovery stay duration of in-patient motor victims in Spain

Santolino

Bolancé

Alcañiz

2012

Accident Analysis & Prevention

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Discrete distributions when modeling the disability severity score of motor victims

Cited by 25 publications

References 50 publications

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking

Modeling traffic crash rates of road segments through a lognormal hurdle framework with flexible scale parameter

Factors affecting hospital admission and recovery stay duration of in-patient motor victims in Spain

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