Probabilistic Modeling of Car Traffic Accidents
Simone Göttlich, Thomas Schillinger, Andrea Tosin
Source abstract
Abstract. We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential equations, we study this stochastic process in terms of its statistical moments and large-time trend. Moreover, we derive analytically the probability density functions of the times of occurrence of traffic accidents and of the time elapsing between two consecutive accidents. Finally, we demonstrate the suitability of our modeling approach by means of numerical simulations, which also address a comparison with real data of weekly trends of traffic accidents.
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