The Poisson probability distribution, first described by Siméon Poisson in 1838, is widely used to model and simulate many real events. It is especially useful to describe low frequency events, and for higher-frequency events it becomes very similar to a Gaussian probability distribution.
What Is The Poisson Distribution?
The Poisson probability distribution is used to describe discreet events, such as number of defects per metre, number of mortgages granted per week, or the number of times a server is accessed per second. When the average number of events for a given unit is known, it is possible to estimate the probability that the event will occur any other number of times.
The Poisson distribution has the property that the standard deviation is a function only of the mean: