Question

Define the concepts of the Poisson process Give example (s) in relatable terms.

Answer 1

The Poisson process is one of the most widely-used counting processes. It is usually used in scenarios where we are counting the occurrences of certain events that appear to happen at a certain rate, but completely at random (without a certain structure).

For example, suppose that from historical data, we know that earthquakes occur in a certain area with a rate of 2 per month. Other than this information, the timings of earthquakes seem to be completely random. Thus, we conclude that the Poisson process might be a good model for earthquakes.

In practice, the Poisson process or its extensions have been used to model.

−− the number of car accidents at a site or in an area;

−− the location of users in a wireless network;

−− the requests for individual documents on a web server;

−− the outbreak of wars;

−− photons landing on a photodiode.