Generalizations of Poisson Process in the Modeling of Random Processes Related to Road Accidents

The stochastic process theory provides concepts and theorems that enable us to build probabilistic models concerning accidents. A crucial role in the construction of the models plays a Poisson process and its generalizations. The non-homogeneous Poisson process and corresponding non-homogeneous compound Poisson process can be applied for modeling the number of road, sea and railway accidents in the given time intervals. Those stochastic processes are used for modeling the road accident number, and number of injured people and fatalities. Poisson distribution and its associated Poisson random process have found applications in various fields of science and technology. A Poisson process and its extensions are used in safety and reliability problems. A counting process is said to be non-homogeneous Poisson process defined by an intensity function. The process is the stochastic process with independent increments, the right continuous and piecewise constant trajectories.