A probability model used where discrete events occur in an apparently random manner, subject to an observable average rate.
This rate parameter is the only parameter required to specify fully the probability distribution function of a Poisson random variable.
For example, the number of business interruptions occurring in a given time period, or the number of admissions to a hospital A & E department in a given time period.
The Poisson distribution can be an appropriate model for processes where:
- Continuous observation is needed, rather than a finite number of independent trials.
- The random variable takes a positive whole number (integer) value, with no upper limit.
- The expected number of occurrences is known or can be estimated, and
- Primary interest is in the number of times an event occurs within a particular period.