Modelling road accident blackspots data with the discrete generalized Pareto distribution

• Published in: Accident analysis and prevention 2014-10, Vol.71, p.38-49
• Main Authors: Prieto, Faustino, Gómez-Déniz, Emilio, Sarabia, José María
• Format: Article
• Language: English
• Subjects: Accident analysis; Accident blackspots; Accidents; Accidents, Traffic - mortality; Accidents, Traffic - statistics & numerical data; Binomial Distribution; Biological and medical sciences; Blackspot; Complex systems; Discrete generalized Pareto distribution; Discrete Lomax distribution; Environment Design - statistics & numerical data; Humans; Mathematical models; Medical sciences; Miscellaneous; Models, Statistical; Prevention and actions; Probability theory; Public health. Hygiene; Public health. Hygiene-occupational medicine; Road traffic networks; Roads; Spain; Traffic engineering; Traffic flow
• ISSN: 0001-4575; 1879-2057
• DOI: 10.1016/j.aap.2014.05.005

•We focus on the modelling of road accident blackspots data.•The discrete generalized Pareto model can be useful for modelling number of crashes.•The discrete Lomax distribution can be useful for modelling number of fatalities.•We consider Spanish blackspots data, from Spanish General Directorate of Traffic.•Both models proposed outperform negative binomial model with those datasets. This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003–2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov–Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed.