Poisson point process
A Poisson process is a stochastic process. It counts the number of occurrences of an event leading up to a specified time. This is a counting process where the increments of time are independent of one another (the times do not overlap).
Definition
The counting process known as the Poisson process is defined as:
- N(0) = 0.
- N(t) has independent increments.
- The number of arrivals in any window of time follows a Poisson distribution.
Where N(t) is the total number of events that occur by time t.
Poisson Point Process Media
5 random Poisson Process
A visual depiction of a Poisson point process starting
According to one statistical study, the positions of cellular or mobile phone base stations in the Australian city Sydney, pictured above, resemble a realization of a homogeneous Poisson point process, while in many other cities around the world they do not and other point processes are required.
Graph of an inhomogeneous Poisson point process on the real line. The events are marked with black crosses, the time-dependent rate \lambda(t) is given by the function marked red.
