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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00446 |
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| _version_ | 1866915289246990336 |
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| author | Göttlich, Simone Schillinger, Thomas Tosin, Andrea |
| author_facet | Göttlich, Simone Schillinger, Thomas Tosin, Andrea |
| contents | 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 modelling approach by means of numerical simulations, which address also a comparison with real data of weekly trends of traffic accidents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic modeling of car traffic accidents Göttlich, Simone Schillinger, Thomas Tosin, Andrea Physics and Society Probability 65C20, 76A30 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 modelling approach by means of numerical simulations, which address also a comparison with real data of weekly trends of traffic accidents. |
| title | Probabilistic modeling of car traffic accidents |
| topic | Physics and Society Probability 65C20, 76A30 |
| url | https://arxiv.org/abs/2410.00446 |