Poisson Distribution
The distribution on models the number of events occurring in a fixed interval of time or space at a constant mean rate :
The probabilities sum to since .
Definition 2.24 (Poisson Distribution)
A Poisson distribution models the number of events occurring in a fixed interval of time or space, where these events occur with a known constant mean rate and independently of the time since the last event.
The Poisson distribution with parameter is defined by
Note that
Limit of binomial probabilities
Consider the number of customers arriving at a shop during , and discretise the interval into with , each subinterval carrying a small probability of a customer arriving. Then
Poisson probabilities therefore arise as limits of binomial probabilities.
Related
Stated in
- Definition 2.24 (Poisson Distribution)§2.5 Discrete Probability Distributions