Poisson Distribution

The Poisson distribution returns a whole-number count of independent events in a fixed period: arrivals in an hour, defects in a batch, calls in a shift.

Write Poisson(mean), where the single parameter is the average count:

Poisson(5)

averages 5 events, sometimes fewer and sometimes more. Use it for a per-period quantity, such as the number of orders that arrive in a scheduled batch. It pairs naturally with the exponential: when counts per period are Poisson, the gaps between events are exponential.