# Statistics - Poisson Distribution

The Poisson distribution is a discrete probability distribution (of count) that expresses the probability of a given number of events (count) that will occur in an interval on a Poisson process

Like the Gaussian and binomial model (distribution), the Poisson is a member of the exponential family of distributions

## 3 - Example

For instance, suppose someone typically gets 4 pieces of mail per day on average.

There will be a certain spread:

• sometimes a little more,
• sometimes a little less,
• once in a while nothing at all.

Given only the average rate, for a certain period of observation (pieces of mail per day, phone calls per hour, etc.), and assuming that the process, or mix of processes, that produces the event flow is essentially random, the Poisson distribution specifies how likely it is that the count will be 3, or 5, or 11, or any other number, during one period of observation. That is, it predicts the degree of spread around a known average rate of occurrence

## 4 - Interval

The Poisson distribution can be used with time and/or space intervals.

• time,
• distance,
• area
• volume.