Poisson distribution

A Poisson distribution is a probability distribution of events over a fixed amount of time or space for events given that the events occur independently of the previous events and the probability of the event is not changing over time. The distribution is usually denoted by Po, with a lambda (λ) denoting the average number of events in the interval. If the Poisson distribution for an event is known, then the probability of that event's occurrence at a specific number can be calculated with the probability mass function for a Poisson distribution. Practically speaking this distribution is not only useful to predict the amount of important events e.g. number of X-rays ordered by the emergency room on a daily basis, but also for much salient modeling in physics e.g. radioactive decay, or quantum noise.

History and etymology

Poisson distribution is named after the mathematician and physicist Siméon Denis Poisson and only coincidentally often resembles the body of a fish.