Nonhomogeneous poisson process and compound poisson process in the modelling of random processes related to road accidents

• Autorzy: Grabski Franciszek

Identyfikatory

DOI

10.2478/kones-2019-0005

• Języki publikacji: EN

Abstrakty

EN

The stochastic processes theory provides concepts and theorems that allow building probabilistic models concerning accidents. So called counting process can be applied for modelling the number of the 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 new theoretical results regarding compound Poisson process are presented in the paper. A nonhomogeneous Poisson process and the corresponding nonhomogeneous compound Poisson process are applied for modelling the road accidents number and number of injured and killed people in the Polish road. To estimate model parameters were used data coming from the annual reports of the Polish police [9, 10]. Constructed models allowed anticipating number of accidents at any time interval with a length of h and the accident consequences. We obtained the expected value of fatalities or injured and the corresponding standard deviation in the given time interval. The statistical distribution of fatalities number in a single accident and statistical distribution of injured people number and also probability distribution of fatalities or injured number in a single accident are computed. It seems that the presented examples explain basic concepts and results discussed in the paper.

Słowa kluczowe

EN

road accident; nonhomogeneous Poisson process; nonhomogeneous compound Poisson process

• Wydawca: Łukasiewicz Research Network - Institute of Aviation ; European Science Society of Powertrain and Transport KONES Poland ; Wydawnictwo Instytutu Technicznego Wojsk Lotniczych
• Czasopismo: Journal of KONES
• Rocznik: 2019
• Tom: Vol. 26, No. 1
• Strony: 39--46
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Grabski Franciszek

• Polish Naval Academy, Department of Mathematics and Physics Śmidowicza Street 69, 81-127 Gdynia, Poland

Bibliografia

• [1] Di Crescenzo, A., Martinucci, B., Zacks, S., Compound Poisson process with Poisson subordinator, Journal of Applied Probability, Vol. 52, No. 2, pp. 360-374, 2015.
• [2] Fisz, M., Probability and Mathematical Statistics, PWN (in Polish), Warsaw 1969.
• [3] Grabski, F., Semi-Markov models o reliability and operation, IBS PAN (in Polish), Warsaw 2002.
• [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] Grabski, F., Nonhomogeneous Poisson process application to modelling accidents numberat Baltic waters and ports, Journal of Polish Safety and Reliability Association, Vol. 8, No. 1, pp. 39-46, 2017.
• [6] Grabski, F., Nonhomogeneous stochastic processes connected to Poisson process, Scientific Journal of Polish Naval Academy, 2 (213), pp. 5-15, Gdynia 2018 (LIX).
• [7] Limnios, N, Oprisan, G., Semi-Markow Processes and Reliability, Birkhauser, Boston 2001.
• [8] Shiryayev, A. N., Probability, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1984.
• [9] Symon, E., Wypadki drogowe w Polsce w roku 2017, Wydział Opiniodawczo-Analityczny Biura Ruchu Drogowego Komendy Głównej Policji, Warszawa 2018.
• [10] Symon, E., Wypadki drogowe w Polsce w roku 2018, Wydział Opiniodawczo-Analityczny Biura Ruchu Drogowego Komendy Głównej Policji, Warszawa 2019.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).