inhomogeneous Poisson process

Finally, the spike rate is used to generate spikes according to an inhomogeneous Poisson process.

Traffic on the AT&T long distance network was shown to be described by a inhomogeneous Poisson process with piecewise linear rate function.

In general, the rate parameter may change over time; such a process is called a non-homogeneous Poisson process or inhomogeneous Poisson process.

Write N(t) for the number of events by time t. A stochastic process is an inhomogeneous Poisson process for some small value h if:

Inhomogeneous Poisson process have been shown to describe numerous random phenomena including cyclone prediction, arrival times of calls to a call centre in a hospital laboratory and call centre, arrival times of aircraft to airspace around an airport and database transaction times.

In comparison to a time-based inhomogeneous Poisson process, the extension to a space-time Poisson process can introduce a spatial dependence into the rate function, such that it is defined as , where for some vector space V (e.g. R or R).