Poisson Distribution

The Poisson distribution models the number of times a rare, random event happens in a fixed window of time or space, given an average rate. Think of calls arriving at a help desk per hour, typos per page, or server errors per day.

It is the go-to distribution for counts of independent events with no fixed upper limit, which is common in operations and web analytics. A quirky and useful feature is that its mean and its variance are equal (both the rate, lambda), so if real count data is far more spread out than its average, a Poisson model is probably too simple.