Affiliation:
1. Polish Naval Academy , Department of Mathematics and Physics , Śmidowicza 69 Str., 81-127 Gdynia , Poland
Abstract
Abstract
The stochastic processes theory provides concepts, and theorems, which allow to build the probabilistic models concerning accidents. “Counting process” can be applied for modelling the number of road, sea, and railway accidents in the given time intervals. A crucial role in construction of the models plays a Poisson process and its generalizations. The nonhomogeneous Poisson process, and the corresponding nonhomogeneous compound Poisson process are applied for modelling the road accidents number, and number of people injured and killed in Polish roads. To estimate model parameters were used data coming from the annual reports of the Polish police.
Reference11 articles.
1. [1] Di Crescenzo A., Martinucci B., Zacks S. Compound Poisson process with Poisson subordinator. Journal of Applied Probability Vol. 52, No. 2, p. 360-374, 2015.10.1239/jap/1437658603
2. [2] Fisz M. Probability and Mathematical Statistics, Warsaw PWN; (in Polish) 1969
3. [3] Grabski F. Nonhomogeneous Poisson process and compound Poisson process in modeling of random processes related to road accidents. Journal of KONES Powertrain and Transport, Vol.26, No.1 2019. Pp 39-46.10.2478/kones-2019-0005
4. [4] Grabski F. Semi-Markov Processes: Applications in Systems Reliability and Maintenance Elsevier; Amsterdam, Boston, Heidelberg, London, NewYork, Oxford, Paris, San Diego, San Francisco, Sydney, 2015.
5. [5] Grabski F. Nonhomogeneous Poisson process application to modelling accidents numberat Baltic waters and ports. Journal of Polish Safety and Reliability Association; volume 8, number 1, p. 39-46, 2017.