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Accid Anal Prev. 2014 Oct;71:38-49. doi: 10.1016/j.aap.2014.05.005. Epub 2014 May 27.

# Modelling road accident blackspots data with the discrete generalized Pareto distribution.

### Author information

1
Department of Economics, University of Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain. Electronic address: faustino.prieto@unican.es.
2
Department of Quantitative Methods and TiDES Institute, University of Las Palmas de Gran Canaria, E-35017 Las Palmas de G.C., Spain.
3
Department of Economics, University of Cantabria, Avenida de los Castros s/n, E-39005 Santander, Spain.

### Abstract

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.

#### KEYWORDS:

Accident blackspots; Complex systems; Discrete Lomax distribution; Discrete generalized Pareto distribution; Road traffic networks

PMID:
24878693
DOI:
10.1016/j.aap.2014.05.005
[Indexed for MEDLINE]